Verbs

No, "should" is not a verb. It is a modal auxiliary verb used to indicate obligation, necessity, or advisability.

walk,run,dance,sing,jumping,fly,watch,washing,swim,talking,writing,typing,riding,eating,directing
finding,catching,kissing,hugging,sleeping,blowing,pressing,cleaning,climbing,breaking,

Smoke can function as both a noun and a verb. As a noun, it refers to the visible vapor and gases given off by a burning or smoldering substance. As a verb, it means to emit smoke or to inhale and exhale cigarette or pipe tobacco.

Is is the verb in your sentence.

future perfect.

S + will + have + past participle

They will have completed the exam by lunch time.

Simply, the past tense word of "understand" is "understood".

For example:

The class "understood" what they were being taught.

The present simple tense of the verb "clean" is "clean" for the pronouns I, you, we, and they (e.g., I clean the house every day). For the pronouns he, she, and it, it is "cleans" (e.g., She cleans the dishes after dinner).

Yes, the contraction should've is a verb, a shortened form for the verbs 'should' and 'have'.
The contraction functions in a sentence as a verb or auxiliary verb.

Example:
We should have planned a little better.
We should've planned a little better.

I imagine that by "base form" you mean the "infinitive" of a verb. If the infinitive does not have the preposition "to" before it, it is referred to as the "bare infinitive". At least, that's the terminology I've come across when teaching English to foreigners.

You use "their" when referring to a group of people or when the gender is unknown. You use "his" when referring to a singular male and "her" when referring to a singular female.

No. "Needn't" is a contraction for "need not," which are a verb and an adverb.

The plural form of "Mary" is "Marys."

The past tense is dealt.

Minor can be a verb depending on how it is used. She'll start school soon, majoring in biology and minoring in Spanish. (minor = verb) He cannot drink because he is a minor. (noun) I am late because I had a minor accident. (adjective)

You need. You is a pronoun; need is a verb.

I appeared fierce to my opponents after tearing apart a noodle with one hand.

Past tense. He received the parcel last week.

"He has received" is the present perfect tense. "He had received" would be the past perfect, and "he received" is past tense.

"have seen" is the verb, and it is in the present perfect tense.

Yes. It's a helping verb, also known as a modal auxiliary.

Indirect objects are best seen as having the word 'to' omitted. In "He gave him an apple" the direct object is 'an apple' and the indirect object is 'him'. It really means 'to him'. So indirect objects are nouns or pronouns.