Assuming these vampires are genetically altered humans and not undead humans. What biological structure changes would you need to make vampires with the following parameters realistic.
Abilities:, ability to see in the dark, regeneration and immunity to most diseases, increase speed, increase strength.
Outside appearances: long fangs, claws.
Weaknesses: some sort of allergic reaction to have garlic, skin burns in direct sunlight.
See in Dark
There are two possibilities here. The more plausible is that vampires have an abnormally large number of rod cells. These would give improved but not perfect night vision and would allow vampires to see by the light of the moon but probably not in pitch blackness. The rod cells would probably cause there eyes to work poorly in bright light this shouldn't be a problem for a species that can't go outdoors during the day. Sunglasses should also counter this disadvantage. The other possibility is a layer of reflective cells behind the eye which strengthens the signal coming to the eye, this is how cats see at night but humans are unlikely to evolve this as the brain would have to change structure.
Regeneration
I suppose a vampire could have improved clotting to heal cuts but this would bring a risk of blood clots. The could also have faster cell regrowth however this would require more energy and make cancers a larger risk.
Immunity
Not true immunity but many bats live with a low level of many diseases like ebola and can survive it by reducing their immune system so although they get ill it is such a weak illness that they can ignore it. This wouldn't work against common cold and other viruses but against some bacterial diseases would be effective.
Speed/Strength Remove the restrictions on how much muscle mass the body could use at once. This would make the vampires stronger but more at more risk of injury and mussel damage. Still, removing a small amount of the restrictions and increasing mitochondria and muscle recovery would possibly make this viable with some strength increase.
Fangs
Lengthening the front teeth and moving the upper jaw forward whilst removing molars and wisdom teeth should work.
Claws
Probably just long, thick fingernails. Would be a bit fragile but over time they would grow back. Thickened, ridged nails would be stronger and still feasible.
Garlic
Garlic has a common allergy causing inflammation and rash to people rubbing against garlic skin. The vampires could have an extreme version of this.
Sunlight
Many pale skinned people already burn easily in sunlight. Obviously this isn't as major as burning to death but often vampires have chalk white skin suggesting a lack of protective pigments so they will burn. Combine this with the increased cell regeneration rate and you get instant cancer for vampires outdoors.
If you wanted your vampire to have regeneration along with near immortality, there are actually many animals in nature with a few different mechanisms to stop aging and/or increase healing. I actually did two short studies on this idea several years ago, so sorry if I start going on a bit of a tangent.
The problem of regeneration isn't that difficult to solve; the real trouble comes from preventing things like cancer from developing. As the organism gets older, the number of mutations in its cells will increase until it inevitably is unable to survive.
I personally think the best solution to this in nature is found in several species of lobster; while not immortal, it makes them long-lived, cancer-free, and mostly immune to radiation. The gist of the adaptation works because most DNA damage occurs at the ends of dna strands; to solve this, lobsters continuously create a protein called telomerase that adds a short cap of base pairs to the ends of dna, drastically improving mutation resistance.
Another solution (though not a very original one) that would work pretty well with the established mythos is to have them enter a healing coma-like sleep occasionally. In this state, they might dehydrate their cells to near-death in order to reduce chemical reactions and decay. This is mainly the same process used by tardigrades (water bears).
Finally, and possibly most interestingly, there exist a few species of jellyfish that respond to aging and massive physical trauma by slowly regressing to a juvenile state over the course of their lifetimes, before turning around and aging to an adult as normal. This has some pretty cool side effects:
Again, I know that this only answers a small portion of the question and is probably a bit more than you wanted, but I have a pretty strong interest in the subject.
Likely retractable, so that they do not get damaged during everyday use. They would likely replace fingernails.
Probably not unlike a cat or snake, which would mean that Vampires would have fewer teeth (as they would no longer need Molars etc. if they live solely on blood). They would have other smaller fangs in order to help grip their prey whilst they drink the blood. They may also inject a venom to paralyze their victim and make them resist less to having their blood sucked from their body.
This might mean their face is more protruding and their mouth is bigger, in order to be able to clamp onto their prey better in order to stop them escaping once their teeth are sunk into their victim's flesh.
This already exists in humans. There are a number of different genetic diseases that cause people's skin to react badly to UV rays, Phytophotodermatitis being one such disease, and they cause differing levels of severity of reactions.
Not unheard of, but very rare in humans. Vampires being allergic to garlic may mean they are also allergic to onions, though the two seem to be linked this doesn't necessarily mean anyone with one allergy immediately has the other. Could, at worse, cause anaphylactic shock if ingested.
Humans can see in the dark, but not as well as owls. This is due to the fact they have very large eyes in proportion to their body. This means Vampires would need much larger eyes in order to be able to see better than humans in the dark. Their pupils will also likely react much quicker to change in light levels, as too much light could probably easily blind them when their pupils are fully dilated.
So far we've tackled most things on your list without having to change anything outside the realms of possibility, as they all already exist in some form or other in either humans or other animals. The rest of the things, however, would need to be stretched slightly in order to achieve Vampirism.
Immunity to diseases
To have an immune system that fights off everything, it would be difficult not to develop an autoimmune disorder, which attacks healthy tissue as well as diseases. It's unlikely that every Vampire would be resistant to every disease without any side effects.
Increased Strength/Speed
Brian Shaw is the current World's Strongest Man, and the guy is a 6'8" colossus. Not really inconspicuous, as Vampires would need to be. So unless you want to have not all vampires stronger than all humans, they may have a more wiry strength like a lightweight boxer.
This requires technique as well as strength, which means that Vampires would still need to practice rather than just be naturally strong. This would be the same with speed. Usian Bolt has incredibly long legs and is very tall, but again it is mostly technique, so training would be required to outpace humans.
The only thing that I can suggest to fix all of these things at once is that Vampires are simply able to fix their muscle cells faster with handwavium (or whatever information you can get over from Biology SE for cells recovering quicker).
This would mean that Vampires can train longer and harder than humans, allowing them to achieve great physical feats much easier than we can. This means better stamina, better strength, better speed, better technique from the extra time put into training, and quite possibly better resistance to diseases.
