I have a PCR product which is 55bp long and I want to sequence it. However, it is apparently too short to sequence, so my sequencing facility reccommended that I should clone it into a plasmid vector, and then send it to them for sequencing.

I generated the PCR product using Tfl polymerase that creates 3'A tails (like Taq). my lab has a TA cloning kit (Invitrogen) which is 2 years old, but was stored at -70C. So I could use the kit to clone my PCR product.

I have several questions:
1) Do you think I can still use this old kit ? Should i perform the controls such as self ligation of the vector and also check the cells for competency?

2) Do you think i can clone in such a short PCR product?

3) Also my PCR does not only make 55bp bands (there are other bands sometimes), so I usually run my PCR product on 12% acrylamide non-denaturing gel, and then I excise the band of the right size, and then i elute it overnight in TE buffer at 37C with shaking.
Can this type of gel purification degrade 3'A tails of my PCR product??

If you have any suggestions, please help me. Thank you so much, I appreciate you taking your time to answer me.