Yes, the governor would appoint a senator for the rest of Session’s term. The Governor, Senate and House of Alabama are Republicans.
Not according to this: Link
Luckily the break between R & D in Alabama is 65% to 35% so its’s not a real issue.
Alabama
If there is a vacancy in the Alabama Legislature, a special election must be conducted in order to fill the vacant seat. The governor must call for a special election if the vacancy happens before the next scheduled general election and the Legislature is in session.[2][3] The governor has all discretion in setting the date of the election along with the nominating deadlines.[3]
https://ballotpedia.org/How_vacancies_are_filled_in_state_legislatures