You can never know for sure if a tree is safe. You can hope that the owners have had it checked and pruned accordingly, but if you're worried, stay in the area of the house furthest away from it.
As a prepper who has been in a red warning before (and sustained some damage) here are my tips.
If it is still safe to go out and do so, move your wheelie bins to your back garden (if you have one) and move your cars away from the house if possible (roof tiles falling can go through windscreens)
Get torches, batteries, candles and matches and put them somewhere you can find them easily if your power goes off. Keep a torch next to the bed.
Get everything on charge now. Phones, powerbanks, ipads, switches, headphones etc.
Yes, filling the bath is a good idea. Also, fill any empty bottles you have. Boil the kettle and fill a couple of flasks. Fill hot water bottles (check the neck of your hot water bottle for the date)
Fill a pan of water and put it on your gas hob if you have one so it can be boiled if you need it. Note: some gas hobs need an electrical supply to ignite.
Get all your warm blankets ready in case your heating goes off. Ditto extra layers and warm socks etc.
Close all of your blinds and curtains. At least if any debris hits your windows and breaks them, this will limit the amount of glass that enters a room.
This is not intended to be scaremongering. It's simply things I've learned from having sustained damage in the past.
Also, if your area says don't travel unless you have to, then really, don't. We all think we need to do things sometimes, but actually staying home and safe is the best thing. Plans can be rearranged.
Lovely to see you here, @OhYouBadBadKitten my lovely x
Stay safe, all.