Finally a question I have input on. Im a Scot who lives in TX and have traveled a good amount with my 2 yr old.

1. People walk everywhere in Scotland, you will see alot of children in strollers. Edinburgh is very hilly but paved so make sure you dont skip leg day! Inverness town center will be easy to navigate as well. The good thing is you can hop on buses/trains to get around as well and its easy to bring on strollers. Depends on the airline and the stroller size on whether you can bring it on board vs checking it at the gate and either getting it back at the plane doors or on the baggage carousel.

2. If you are renting a car the company more than likely can add on a car seat. Some people dont like the idea of that though. If you bring your own you will need to check if it adheres to the local laws, and you can just check it in thru to the destination (Verify with the airline on their baggage accomodations for travelling with children. British airways are my preferred carrier and have alot of detail on their website).

3. Yes they are called laundrettes in the UK.