are tamper resistant receptacles required when rewiring an old house
I'd use TR receptacles in any case. Here in Tennessee, if I were to pull a permit to do this, yes my jurisdiction wants permits for anything and everything electrical, I would most definitely have to use TR outlets. They aren't much more in expense compared to a standard receptacle.

It's not overkill and I personally would prefer to err towards safety and/or over protection. This will also prevent any issues down the road as far as codes are concerned.

Edit: (Brain fart)

Not sure about carbon monoxide detectors, but hardwired smokes are required.

As for your outdoor receptacles, they do need weatherproof covers but the type of cover will depend on location. Weatherproof ( bubble ) covers should be used if a receptacle is located where there's no overhead protection or if a receptacle is installed, say on a covered porch, but the receptacle is 3' or less away from the edge of the covering roof.