I am new to LHE and 2p2. From my understanding there is early, middle and late position. In the early position, there are three situations: SB, BB, and UTG. I believe tighter starting hand ranges are played from the early positions. Will the starting hand ranges vary between the SB, BB, UTG?

I dont play LHE much, but you are looking at this wrong. UTG is early position when relating to starting hands. When you are in the blinds preflop, you get to see everyones actions at the table prior to making your decision. In LHE, I am assuming you are going to be getting very good odds frequently to play a wider range of cards out of the blinds. Contrary, you should be playing a narrower range from UTG not only because you are out of position post flop, but you are out of position preflop as well.

You need to learn the crucial distinction here. Pre-flop, UTG is first to act, and the blinds are last. Although the blinds have already been forced to put money in the pot, they get to see what other players do. The blinds can then enter the pot at a discount price, or even (in the case of the big blind) check their option and see a free flop (if everyone limped). In limit hold'em especially, the blinds will often have great pot odds to see a cheap flop. But weighing against that meagre benefit is that they will have to act first on every subsequent street.
Hand ranges for both the blinds and early position players should generally be very tight. Not only is it very difficult to play a hand without having information on how weak/strong the other players are (based on their betting action), but the blinds and EP players cannot control the pot size. Even if they flop a monster hand, it's hard to get paid off, because if they bet, other players may fold, and if they check (hoping to slowplay or check-raise) the players after them may check behind.
There are plenty of hand charts available if you hit google and specify fixed limit poker. You can also look in the FLH sub-forums. But it's absolutely crucial that you learn how betting rounds are structured both pre-flop and post-flop, because position is incredibly important in all forms of hold'em.

Here is a link to a useful library of posts on LHE subjects, I hope you find a lot you can use in here:

** Micro Limit Library **