Offset blog address confusion

I want to have the blog as a subset of our main website so I have set up the directory as https://www.website.com/weblog/. I get a basic index page but without the css and a number of error messages, such as:
Database error: [Unknown column ‘category_nicename’ in ‘field list’]
SELECT DISTINCT ID, category_id, cat_name, category_nicename, category_description, category_parent FROM wp_categories, wp_post2cat, wp_posts WHERE category_id = cat_ID AND post_id = ID AND post_id IN (1)
Warning: Invalid argument supplied for foreach() in /var/www/html/weblog/wp-blog-header.php on line 478
Database error: [Unknown column ‘comment_approved’ in ‘on clause’]
SELECT ID, COUNT( comment_ID ) AS ccount FROM wp_posts LEFT JOIN wp_comments ON ( comment_post_ID = ID AND comment_approved = ‘1’) WHERE post_status = ‘publish’ AND ID IN (1) GROUP BY ID
up front and
Filed under:
Database error: [Unknown column ‘category_nicename’ in ‘field list’]
SELECT category_id, cat_name, category_nicename, category_description, category_parent FROM wp_categories, wp_post2cat WHERE wp_post2cat.category_id = cat_ID AND wp_post2cat.post_id = 1
Warning: Invalid argument supplied for foreach() in /var/www/html/weblog/wp-includes/template-functions-category.php on line 65
after “Hello World!”
What do I need to change to fix this?