Regardless of whether you have a helium valve or not, if you plan to wear your watch in water (swimming, showering, heavy rain, etc), you should have it pressure-tested (at least) yearly to be sure the case is sealed.
Pics not sufficient to properly qualify the case (but looks similar to most aftermarket cases), but the bracelet is clearly low-end. Were it me, I would stick with DW, Phong, NDtrading or Yuki.
Bake them in middle of your oven at 500 degrees for (up to) 20 minutes. Keep an eye on the oven & remove the hands the second they reach the desired color (the line separating beautiful & burned is very thin). For a darker color, apply a bit of iodine to the backside of the lume before baking. This is art, not science.
TT is not my thing, but this 1 looks good to me. That said, always buy the seller 1st (check out references & previous Rolex sales history to reduce the likelihood of being taken by a pretty face).
5512 = Chronometer spec Submariner - usually (but not always) has 4 lines of text in the bottom half of the dial
5513 = Non-chronometer spec Submariner - has 2 lines of text in the bottom half of the dial
5514 = 5513 made specifically for Comex - often (but not always) contains a Comex signature in the bottom half of the dial & (usually) a Helium exhaust valve in the side @ 9 o'clock
(This is a gen-powered franken that I constructed a couple of years ago - it is not available from any rep seller)
It sounds like the movement is out of beat (the hairspring/collet is misadjusted/off-center, causing the balance to require more force to start it moving). Your watch requires servicing.
Looks good, but I would have the dial relumed so the lume does not reflect light (some 50s Rolex dials did have a glossy finish, but the radium or tritium, which was applied after/on top of the dial finish, should not)