There are a number of options here:
2. If May resigns, then Corbyn would be given the chance to form a government.
3. There are other options that do not involve seeking to form a coalition government: May could attempt to enter into a ‘Confidence and supply; agreement with smaller partys. This would mean that the smaller parties, while not getting ministerial positions, would get some concessions to their chosen policies in return for voting with the Government the smaller parties would support the government on financial matters like the Budget, and in confidence votes which would otherwise bring the government down.
4. Finally, and probably the worst option for a Country trying to navigate a Brexit, the leader in seats could just opt for a minority government and try and negotiate each and every time with minor parties or risk being voted down at every single opportunity. Minority governments rarely last long.
In 2010, the Conservative and Lib Dem coalition took 5 days to form, but that was hurried along by significant risk in financial markets. This is widely thought of as being too hasty so dont expect a repeat here.
Could we get another vote?
Highly unlikely due to the Fixed Term Parliaments Act, which holds that if a government loses a confidence vote, alternative PM’ss get a 14 day period in which to form a Government