The te form

[mike16]

What is the proper use of the te form in endings?

For example in mite kudasai turned negative is minaide kudasai
In another mite imasu turned negative is mite imasen

However I stumbled upon a sort of suggestive form which is done by adding wa ikaga/dou desu ka to the te form and translates the verb to suggestion of the verb, example:

eiga o mite wa ikaga desu ka
Translation: How about we watch a movie?

The question is what is more appropriate if I were to give a negative suggestion for example, How about we skip (not eat) lunch?

would I say:

hirugohan o tabete wa ikaga dewa arimasen ka

or

hirugohan o tabenaide wa ikaga desu ka

or is there something else about giving a negative suggestion? or is both of them applicable in speech?

 

[grapefruit]

What is the proper use of the te form in endings?
For example in mite kudasai turned negative is minaide kudasai
In another mite imasu turned negative is mite imasen

First of all, the "~te (kudasai)" form and the "~te iru (imasu)" form are distinct. The former is used for requesting some action, while the latter is used for describing an ongoing action or resultant state. So, the negative form of "mite kudasai" would be "minani de kudasai", which means "please don't watch/look". The negative form of "mite iru" would be "mite inai (imasen)", which means "is not watching/seeing/looking" or "has not watched/seen/looked".

However I stumbled upon a sort of suggestive form which is done by adding wa ikaga/dou desu ka to the te form and translates the verb to suggestion of the verb, example:
eiga o mite wa ikaga desu ka
Translation: How about we watch a movie?
The question is what is more appropriate if I were to give a negative suggestion for example, How about we skip (not eat) lunch?
would I say:
hirugohan o tabete wa ikaga dewa arimasen ka
or
hirugohan o tabenaide wa ikaga desu ka
or is there something else about giving a negative suggestion? or is both of them applicable in speech?

This is more tricky. Two forms came to my mind: 1) "Hirugohan o taberu no o yamete wa doo (ikaga) desuka?" and 2) "Hirugohan o tabenai no wa doo (ikaga) desuka?"

Form 1) is a combination of applying the "~te wa doo (ikaga) desuka" structure and the verb yameru. The verb yameru means "stop". The possible reason why "verb naide wa doo (ikaga) desuka?" does not work is that "~te wa" in the ~te wa doo desuka does not follow the ordinary "noun" + particle pattern. It is strange to see a verb form without nominalizer like "no" or "koto" in front of wa (e.g. "miru" vs. "miru no/koto wa"). For this reason, the "~yamete wa doo desuka" form must be a set phrase.

Form 2) is a simple combination of "noun" + "wa doo desuka?" and the nagative plain form of "taberu". This is straightforward: "verb plain form" + "no" + "wa".

Also, if you have learned the "tara/ba doo desuka?" structure, you can use "~kattara/nakereba doo desuka."