Yes, they mean the same thing. The second sentence doesn't sound very natural though. It would be better to say "He hasn't eaten any beans, he has just eaten some peas." Hope this helps ^^

Yes, in this situation, 'eat' and 'have' mean the same thing. It is very usual to use the word 'have' in the place of 'eat' or 'drink'. Watch your verb forms, though. 'He hasn't ate' isn't just 'not very natural' - it's completely incorrect. Surely you have studied the basic form of the present perfect tense?