@ kevinb623
First, you should setup your site to suppress all PHP notices on production sites. This is a best practice. See this post for more info on how to do this:
http://aristeides.com/blog/wp-hide-php-errors/
As for the db notices you are seeing. On install Connections should detect this and use the correct table types. For some reason this did not happen for you. Unless this is an older installation of Connections because older versions did not do this check.
To suppress the db notices, go to the Connections : Settings admin page, click the Search tab and disable the FULLTEXT search option.
As for the like_escape notices. They are on my short list to remove now that Connections requires WP 4.1 and newer. They are harmless and they are only for devs. This is to let us know we need to plan on to remove their usage. These notices will go away when you disable the PHP notices as explained in the blog post.
Hope that helps!