Yes, get her to write a letter of invite addressed to you to come to stay with her. It will need to include the full address plus her full name and Thai ID number.
If you bought a Tourist Visa from a Thai Embassy/Consulate outside Thailand before you entered you get your extension from the main Immigration Office at Chaengwattana, Building B, Counter J. If you entered on visa-exempt you are going to go to IT Square, Laksi Plaza (3rd Floor) temporary office, just next to Lak Si station of SRT Dark Red Line. All extensions cost 1900B.
Your airline will possibly ask for proof of onward travel within 60 days as a condition of allowing you to fly. Ask them what their policy is for Visa Exempt entries. If required Google "onward travel ticket".
Renew your insurance (as you would do for an extension) and do a border bounce before your Non-OA expires to get a new 12 month entry stamp. This 12 months will not be multi-entry so a re-entry permit will be required if you plan to travel at some point.
People with visas get denied entry (the visa is issued by the Embassy under the Ministry of Foreign Affairs but Immigration have sole responsibility for entry and things inside Thailand (under the Ministry of the Interior)).