Basically I'm wondering, if I give someone my mobile number will they know my Google+, gmail address, youtube account, etc? Or other apps that are linked with my email or number, such as Facebook or Twitter?
No. They will only know your mobile number. Other internet based things need email account to work and that's separate from your mobile number from the network. Whatsapp may be the only exception here that I know about. Just don't share any passwords with anyone. Ever.