if i were to assume a mortgage, does the lender check my credit and income history?
Depends on the the lender, the type of loan, and when the loan was originated.
These details should be spelled-out in the mortgage/note you plan to assume.
As 71 noted, assuming with or without the need for qualification will be a stipulation included in the original note you intend to assume.
Any FHA loans written before 12-15-89 may be assumed without qualification (investors are excluded from assumption).
Most ARMs are written with an allowance for assumption; the need for qualification depends on factors already mentioned.
very few loans these days are assumable. fha had assumables with no qualification this has gone away.