House Rabbit Community and Store
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The subject of intentional breeding or meat rabbits is prohibited. The answers provided on this board are for general guideline purposes only. The information is not intended to diagnose or treat your pet. It is your responsibility to assess the information being given and seek professional advice/second opinion from your veterinarian and/or qualified behaviorist.
Sorry no one got to this sooner!
I’ve done a little research and it appears that most palms are safe for rabbits, except for a ‘sago palm.’ If you can identify the exact type of trees by your house, it may be easier to research. As for the toys, if they are from a credible seller, such as BB here, you should be fine. I have given my bunnies palm leaves I picked myself, just make sure they are clean and pesticide free and that you let them dry out completely first. 
Blackberry/raspberry, grape and rose vines are fine for bunnies, though I’m not quite sure what the pre-made toys are made out of. You can call the company.