The IP and TCP headers are all contained in the same packet right?
Yes
What are the sizes of the IP header and TCP header?
IP header is usually 20 bytes length, but the actual length is specified in the header itself(http://www.erg.abdn.ac.uk/users/gorry/course/inet-pages/ip-packet.html). Same for TCP header (http://www.wtcs.org/snmp4tpc/images/TCP-Header.jpg) TCP header follows IP header, but IP can be used as transport for many other protocols, UDP, ICMP, GRE and etc…
Does the data/payload section always follow the TCP header?
If TCP packet contains data then yes they follow TCP header.