All I do is 3 gallon stove-top BIAB batches. You are fine with the gear you have, just go to Home Depot or Lowes and buy 5 gallon paint strainer bags in the paint department. Seeing as how your kettle is on the small side, pick up some firmcap and add a drop per gallon before your boil to avoid boil-overs. Also pick up some PH mash stabilizer and add it as prescribed before your mash. On the conversion from 5 to 3 gallons, you can enter your recipe as 5 gallons into brewersfriend. com and convert it to 3 using their handy scale tool. Works like a charm. I ferment my 3 gallon batches in 5 gallon better bottles, no problem. If you are worried, the firmcap will also cut down on foaming and help you avoid blowoffs just use 2 drops per gallon. As for sparging, I don't and I also don't do a mashout... I just remove the bag as it is very manageable and let it drain into the kettle, put it in my bottling bucket and twist the bag to get the wort out of the bag and add it back in before the boil. I then top off to pre-boil vol and begin. I'm hitting 78-80% that way, no problems.
I've been doing a lot of these lately, so if you have any more questions just ask. There is a bit of a learning curve.