There's some great information in this thread... all I'll add if it is not covered above (and it may be) is make SURE you have a GFCI receptacle or breaker for your dedicated circuit.
fwiw, I decided to try a BTA in my 55g w/4-65w PC (against my better judgement)... with optimal water conditions (I mean top notch) and it only lasted about 3-months. My corals have lasted sense I put them in the tank.
Ditto Sea_Star's comments... over the years I have had clowns host a frogspawn, xenia, toadstool & shrooms... all of which should do fine under your lighting.
Even if you were to upgrade your lighting, I'd suggest you wait a minimum of 3-6 months before trying an anemone. 6-months minimum...
135 watts of what?? PCs, VHOs and T5s limit the corals, anemones and clams that you can keep... the MH would allow you to keep about anything... but for a 20g you may not want to keep high light demanding corals anyways.
You can add both at the same time. Typically it's recommended to only add one fish at a time but I think you would be fine adding two Percula Clownfish... especially if they are small. You can add as many cleaners together as you want. Again I don't see any reason not to add your cleaner...