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1) Yes,

sage: L = lie_algebras.sp(QQ,4)
sage: L
Lie algebra of ['C', 2] in the Chevalley basis

If you want a basis try L.basis()

2) you can get this directly from the Cartan Matrix which by definition will get you 2 since h(1)=alphacheck[1] is the coroot associated to alpha[1]. In this particular case you could try

sage: L = lie_algebras.sp(QQ,4, representation='matrix')
sage: L.simple_root(1,L.h(1))
2