I will be the bad guy here....I would NEVER use a potty chair in a room that is NOT a bathroom. I train kids regularly as a home childcare provider and previously a nanny with a combined 23 years experience, plus parenting years as well.
Why teach a child its OK to go potty in a living room, kitchen or hallway???? Thats not the way our world operates and part of toilet learing is normal world functions, rules and control. I am a firm believer in this and follow some of the guidelines in the 3 day potty training method(Lora Jensen) and train kids pretty young now.(22-28 mos generally)
As a provider, licensing requires gates in my house. But I find those younger ones still need my help anyway, so I want to supervise. Little girls don't scoot back far enough on the potty (so will tend to make a mess all over, needing clothes changed, etc) ....boys spray...etc. Many would say then they are not ready to be trained. I disagree and would rather assist then when they tell me they need to go (I NEVER ask them or make them go sit just because a time interval has elapsed and they haven't gone for a time)...then to be changing their diapers.
So my advice is...keep the gates in place when you feel they are needed. Teach your child stair safety when you are right there to supervise. Use gates at night if falling down steps is a concern...and assist them when they say "I gotta go potty" (open the gate and get them where they need to go....make sure they are successful and help wash their hands when done ...this is usually what my 2.5 year olds need help with..the sink!)
Best wishes and CONGRATS on a young trainer!!!! I love seeing that!!!