If you are skittish about trying the method I laid out, you probably will not get the problems fixed. If I remember correctly, the site is overloaded with plugins. The practical limit is about 10, but that site was way over that number. WordPress loads every plugin whenever a page is requested, whether the plugin is activated or not. That can easily drag down the performance. Old plugins and themes that have not been updated cause a lot of problems with incompatible code and conflicts.
Most likely the only way you are going to fix the problems for the long term is to bite the bullet and update everything, including the theme.
"Democracy is two wolves and a lamb voting on what to have for lunch. Liberty is a well-armed lamb contesting the vote." -- Benjamin Franklin