It is often difficult to definitively know whether or not an herbal supplement such as saw palmetto will interact with certain prescription medications. There isn't much data and studies are lacking on potential drug interactions with saw palmetto.
Saw Palmetto - Aspirin Interaction
Having said that, based on your medication list, the one drug that stands out is aspirin and there may be a potential interaction.
There is data that shows saw palmetto might increase the risk of bleeding when used with other agents that do the same. Studies have reported prolonged bleeding times in those taking the supplement along with other blood thinners, such as aspirin.
In terms of other known drug interactions, the most commonly reported interaction with saw palmetto is with hormones and contraceptive drugs. Saw palmetto is known to have an antiestrogenic effect. Based on your drug list, it doesn't appear that you are taking any sort of hormonal product however so this likely isn't a concern.
Additionally, there are known drug interactions between saw palmetto and the following:
5-Alpha Reductase Inhibitors
Propecia (finasteride) is a common medication in this class. Saw palmetto has a similar mechanism of action of 5-alpha reductase inhibitors. The combination of the two could be additive and it is unknown if that could provide extra benefit or could be harmful.
Saw palmetto has antiandrogenic effects and would lessen the effects of androgenic drugs.
Beside aspirin as discussed above, there are no reported interactions between saw palmetto and your medications. This doesn't mean there aren't any, just that there aren't documented cases. Before taking any supplement or herbal product, please reach out to your doctor for their suggestion and direction.
There should be no concern with vitamin E.