1. Wrong: However she decides to finish this game Hotchkiss will certainly win.
Better: However she decides to finish this game, Hotchkiss will certainly win.
Explanation: Here, however is being used to open an introductory adverbial clause, so the clause needs to be followed by a comma. (see rule 11)
2. Wrong: We wanted to go in fact we had already bought our tickets.
Better: We wanted to go; in fact, we had already bought our tickets.
Explanation: In fact can't join these two sentences as a conjunction would, so it needs to be preceded by a semicolon.
3. Wrong: Mr. Bradley would love to give holidays more frequently however he knows the importance of patience.
Better: Mr. Bradley would love to give holidays more frequently; however, he knows the importance of patience.
Explanation: The conjunctive adverb however can't combine two independent clauses as a conjunction could.
4. Wrong: The shoes weren't my size I tried however to shove my feet into them.
Better: The shoes weren't my size; I tried, however, to shove my feet into them.
Explanation: The first independent clause ends after size. The however in the middle of an independent clause needs to be separated on both sides with commas.