Can taking Benadryl (diphenhydramine) for a few months lead to dependency? Dizziness? Palpitations?

No, yes, and no. Benadryl (diphenhydramine) is a good drug for allergy and allergic reactions and, very occasionally, for sleep. If your take it continuously to sleep it can lose it's effectiveness and make it difficult to sleep at all without it. Anything with sedative effects can lead to dizziness. Palpitations are less likely. Moderation is a good idea.