Riding without straps is plain stupid, period. Don't care how long you've commuted w/o them. Gaper central.
My guess is you're at about 55 gear inches with a ~44-21 setup, so yeah 10mph sounds about right.
As for tensioning your chain, here's how you do it on a fixed gear.
- Get yourself a ski sock or a rag.
- Loosen your nuts completely.
- Put the rag just under your brake bridge on the tire.
- Rotate the wheel so the rag starts to "get stuck" between the seatube and the tire.
- Turn the wheel until you have proper tension. Proper tension is a personal preference but the general rule of thumb is 1-2" of play, total, when you move the chain up and down w your fingers. Super tight is never good, it puts strain on your chain, chainring, and cog; eventually wearing them out unnecessarily quick.
- Once you have your tension, center your wheel. I use one hand on the rim/seatube to tension and center.
- Tighten nuts with other hand. Do not over tighten them. If your do, you're putting unnecessary stress on your hub.
You really should never have to readjust unless you are riding a TON. By that I mean thousands of miles. I've been commuting the last 2 years on a $9 KMC chain and have readjusted my chain tension once. I need to adjust again soon, but I'll probably just buy another chain. Chains will stretch a tad after a TON of miles, but by keeping that chain for too long, you're adding additional wear to your chainring and cog. So imo, a $9 clean chain is worth it.