I'm not sure that any of them is wrong, but two of them are stylistically terrible. A native speaker would have no trouble understanding any one of them though. These are the bad ones: #1 the comparison "mosquito as bit" makes little sense. You can't compare a noun to a verb. To fix it, you need to say "mosquito as the one that bit" so you will be comparing a noun with a noun. You can also fix it by using "that" instead of "as". #6 same problem as #1.

1 through 5 are all fine and probably mean the same thing and could be used interchangeably. Technically, 3 and 5 are probably more "correct" than 2 and 4 ("that" is better than "which") if this can be considered a restrictive clause, but I would personally use any of 1 through 5, both in writing, and in spoken English. 6 is not correct. 2 or 4 could possibly be used as a non-restrictive clause following a previous mention of the mosquito, with a comma before "which", but that would be very unusual, and the basic meaning would be the same, just with a slight difference in emphasis and sentence flow.

1. This is the same mosquito as bit you just now. Maybe not acually wrong, but most people (in the US at least) would say: same mosquito as THE ONE THAT bit you, etc. 2. This is the same mosquito which bit you just now. Incorrect, since it's not a subordinate clause. It would only be correct it SAME refered to something other than having bit you. 3. This is the same mosquito that bit you just now. GOOD 4. This is the mosquito which bit you just now. As number 2, WHICH should be THAT, in most cases. 5. This is the mosquito that bit you just now. GOOD 6. This is the mosquito as bit you just now. I think this is fine in the UK, odd in the US. Question: Which is/are grammatically correct? Do they have the same meaning? You might want to study when to use THAT vs. WHICH. Many native speakers have trouble with this as well.

2,3,4 and 5 are correct. They all have basically the same meaning. You might be more likely to use "...same mosquito..." in the sentence if, for example, you had both been bitten by the same mosquito.