I advise her to stop smoking. > Indicative and correct I advise (that) she stop smoking > Subjunctive and correct; the 'that' is optional The second is example is not very common with the verb advise. It is more common to say: I would advise her to stop smoking. > Indicative and correct and common I would advise she stop smoking. > Subjunctive and correct but uncommon With the verb 'suggest' your second option is more common. For example: I suggest she stop smoking. > Subjunctive and correct and common I suggest she to stop smoking > Wrong I would suggest she stop smoking. Correct

Your first sentence is in the wrong tense. These are correct: I advise that she stop smoking. I would advise her to stop smoking. I advised her to stop smoking. I advised [her father] that she stop smoking.

Ok this one is tricky. The way you've written it here, it should be "I'd advise her to stop smoking". But if you make a slight change, "I'd advise she stop smoking" is correct and almost interchangeable. The first one sounds a little more personal. I think it slightly implies that the speaker knows "her". Where the second example does not have that implication.