No way to know about asbestos from here..
You can replace the joists by sistering them but you may still need to replace them because there will undoubtedly be joints in the floor decking directly centered over the old joists.
The rim joists will be trickier.. The rim joist will be under an exterior wall which means it wil be more than likely a load bearing wall. At the very least the rim joist will be supporting the wall itself. The sill plate will also be under pressure. This sort of lifting can cause damage in unexpected places such as; the interior walls can crack, the roofing can actually tear, framing members can break and loads can shift instantly. In other words, this can be a very dangerous job especially when working by yourself. Personally, I refuse this type of work. I can't afford the risk even with insurance. Death benefits are never enough.
I'd get some help on this one and at the very least seek professional advice from someone who can look at the job and point out the dangers and the best way to avoid problems.
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