“Consider”
Sentence 1
Please let me know which input to consider.
Infinitive. The infinitive form of a verb is basically a form that doesn't have to agree with other things in the sentence. It has no person or number, even if it has a subject. An infinitive verb doesn't even need a subject, as in your sentence. If it has a subject, it's in the objective case, as in this sentence:
Let him consider what you have said.
Notice that consider does not agree with him even though him is its subject. A non-infinitive form would be "He considers what you said important." Notice the s to agree with He.
It's debatable whether infinitives have tense. In some languages, they clearly do. In English, it's not so clear. But you can force a tense onto an infinitive like this:
Please let me know which input I was to have considered.
You could say that have is infinitive here (with no tense), or you could say that have considered is the perfect-present infinitive of consider. It's just a matter of which terminology you prefer.
Sentence 2
Please let me know which input should be considered.
This is another infinitive. I'd call it a passive infinitive. But one could also reasonably say that be is in the infinitive and considered is a past participle. We form the passive voice in English with be + past participle.
The reason be (or be considered) is in the infinitive here is because it's governed by the modal verb should. Other common modal verbs that work the same way are: can, could, may, might, must, shall, and will.
“Let”
In both sentences, let is in the present tense and the imperative mood. That is, it's a command, and it's telling the listener to do it now.
“Know”
As you can probably guess now, know in both sentences is in the infinitive. Its subject, me, is in the objective case.
“Should”
Should is in the present tense. Even though it's third-person singular (its subject is input), it doesn't get a terminal -s because modal verbs don't inflect. That is, they use their infinitive form in all situations.
You can verify for yourself that should is in the present tense by replacing it with an ordinary verb and seeing how it inflects. For example, "Please let me know which input is in need of consideration."
By the way, in English, it's customary to list verbs in dictionaries in their infinitive form. This is said to be the "lemma form" of the verb: the basic one, by which you refer to all the forms of the verb. Other languages follow different customs for the lemma; for example, in Latin, the first-person present singular is usually the lemma. But anyway, when you look up a verb in an English dictionary, you'll find it listed in its infinitive form.
