First question: In esperanto it is my understanding that you can arrange subjects nouns and objects in any order, is this right? EG
Mi sxatas gxin
Mi gxin sxatas
Sxatas mi gxin
Sxatas gxin mi
gxin sxatas mi
gxin mi sxatas
Second question: When using a negative, can you move the pronouns in between "ne" and the verb? EG
Can you say "Mi ne gxin sxatas"?
All 6 word orders are correct, but the usual order is "Mi ŝatas ĝin". You can use word orders for emphasis, e.g. "Ĝin mi ŝatas", "I like this one (not another one)".
"Ne" is normally put before the word it negates: "Mi ne ĝin ŝatas" would be understood as "I don't like it (but I like something else)".