1) Hydrogen only has an S orbital, but if you excite an electron in Hydrogen, which orbital or energy level can it go to? Does it have P-orbitals?
Correction: hydrogen only has one electron, which is in the 1S orbital when in its lowest energy state. This electron can be promoted to higher energy states with, for example, absorption of a photon of the correct energy. When excited, this electron can be located in an orbital with a different angular momentum quantum numbers (p, d, etc.).
2) When two atoms combine in Molecular orbital theory, do ALL their atomic orbitals (belonging to all principal quantum numbers, so also the core orbitals) then combine to form molecular orbitals or is it only ALL their valence orbitals?
Strictly speaking, yes, all atomic orbitals are combined to form molecular orbitals, provided they have the right symmetry to interact. In practice, it is possible to consider only the valence orbitals because the overlap of "inner" orbitals between adjacent atoms is very small. Do note that molecular orbitals are mathematical constructs. It is we humans that combine atomic orbitals to form molecular orbitals, which gives us a fair description of where electrons are located and what their energies are.
3) In Methane Hydrogen atoms only have 1S orbitals, so would the S orbitals of Hydrogen then Bond with some P orbitals of Carbon and Some S orbitals in Carbon? Would this not give us different bond lengths?
The bonding structure of a molecule like methane depends on the bonding model you use. In a hybridization approach, the atomic orbitals on the carbon are combined to form hybridized orbitals that have the appropriate symmetry to bond to the hydrogens. A molecular orbital approach is superficially similar, forming molecular orbitals from combinations of all the atomic orbitals. It's pretty clear that there's not a 1-to-1 bonding between hydrogen atomic orbitals and carbon atomic orbitals, because the resulting structure would be completely wrong.
http://en.wikipedia.org/wiki/Orbital_hybridisation