Prep and stain for new and old cedar deck

We live in Minnesota. Our deck is cedar, half full sun/half shade. It gets daily traffic as it's our walkway from our garage to the house. We had problems with mold/mildew on the last stain in the shade area (but never tried to clean it.) We just replaced about 1/4 to 1/3 of our deck with new boards as the old boards were rotting. We also replaced a bunch of boards about 4 years ago due to rot. So the deck now has boards that are either about 15 years old, 4 years old, or brand new. We stripped and brightened the existing boards, but not all of the last stain (I believe it was a Sherwin Williams semi-transparent) was able to be removed despite multiple attempts with remover and a powerwasher, as shown in the photos. We're not looking for picture perfect, all uniform looking boards. Some variation across boards is fine (and I actually kinda think the boards right now look cool with a little bit of red stain as they look like weathered barn wood which fits with our house style!)

Our questions are:

1) Do we need to sand to get rid of all of the existing stain before staining again? (or if we don't is it just an aesthetic thing or will it compromise bonding?)

2) When should we restain since some of the boards are new - in a couple weeks (can't wait longer than that here in MN!) or next spring?

3) What stain would you recommend? From photos we like to look of Timber Oil and it seems like with that we can more easily recoat the walking path that gets worn, and can more easily recoat the whole deck again when we have to replace a few boards. Is that a decent choice or is something like one of your top rated stains better? While some variation in colors between new and old is ok, we don't want that to be totally obvious either.

Thanks much. Super appreciate your expertise and advice!