Importing WP posts (#1054 – Unknown column 'post_category' in 'field list' )

I’m moving my website and blogs from one server to a new server. I have WP installed on both servers. I just went into phpMyAdmin > commsun2_wrdp1 > wp_posts, exported to my hard drive, then on the new cpanel host, I attempted to import into the same file location, however I received the error message #1054 – Unknown column ‘post_category’ in ‘field list’.
I have WP 3.5 installed on the new server, but some of the blog posts on the old server are 6 years old, so likely not WP 3.5.
I also tried to export-import as above another file wp_terms, as that seems to relate to categories, and I was thinking that I don’t have all the old blog categories set up on the new server site….but that didn’t work and I received the following message:
Error

SQL query:

— — Dumping data for table wp_terms — INSERT INTO wp_terms (term_id, name, slug, term_group) VALUES (1, ‘Uncategorized’, ‘uncategorized’, 0), (2, ‘Blogroll’, ‘blogroll’, 0), (3, ‘Nutrition’, ‘nutrition’, 0), (4, ‘Mind Body Medicine’, ‘mind-body-medicine’, 0), (5, ‘Community Acupuncture’, ‘community-acupuncture’, 0), (6, ‘Stories’, ‘stories’, 0), (7, ‘nuts and bolts’, ‘nuts-and-bolts’, 0), (8, ‘Testimonials’, ‘testimonials’, 0), (9, ‘Sustainability’, ‘sustainability’, 0), (10, ‘Peace’, ‘peace’, 0), (11, ‘communichi’, ‘communichi’, 0), (12, ‘seattle’, ‘seattle’, 0), (13, ‘affordable’, ‘affordable’, 0), (14, ‘acupuncture’, ‘acupuncture’, 0), (15, ‘beacon hill’, ‘beacon-hill’, 0), (16, ‘jordan’, ‘jordan’, 0), (17, ‘serena’, ‘serena’, 0), (18, ‘sam’, ‘sam’, 0), (19, ‘amber’, ‘amber’, 0), (20, ‘upel’, ‘upel’, 0), (21, ‘Noodles’, ‘noodles’, 0), (22, ‘facebook’, ‘facebook’, 0), (23, ‘affordable acupuncture’, ‘affordable-acupuncture’, 0), (24, ‘healthcare’, ‘healthcare’, 0), ([…]

MySQL said: Documentation
#1062 – Duplicate entry ‘1’ for key ‘PRIMARY’

Can you please advise? Thank you, Jordan Van Voast