You could say, He went to a hospital and underwent knee surgery, but not "to underwent". To undergo is the verb, "underwent" is past tense.

As Glasguensis says, "will be undergoing" is the future tense, in the continuous / progressive form. I gave the simple form of the future, "will undergo", but should have mentioned that it is indeed in the future tense.

1.Is there any "tense" problem in the sentence. (The perfect tense always needs the past participle of the main verb) 2. Is "undergo" & "encounter" suit able for this sentence ( situation ).

Using "undergo a treatment or procedure" is the way doctors speak, not average people. If you want to use it, please give us the specific example of what circumstance you'd like to do that. Then we can tell you exactly how it sounds to our native ears.

Undergo can refer to unpleasant things but it can also be more neutral - The city has undergone many changes in the past century. Get through implies some sort of struggle and achievement. I hope he gets through his exams.