You seem to be confused on how "would" is used and what it even means. "Would" creates a conditional phrase, not a hypothetical. Hypotheticals are created using the subjunctive mood and often use the conditional in the second clause:
"If I were to eat my lunch, I would remain healthy."
In this sentence, you can't put "would" where "were" is and have it be right. "Were" expresses the past subjunctive mood of "to be." The conditional "would" only happens in the next clause after the comma.
There is nothing that prevents having "would" twice in a single sentence:
If my friend sat here, I would give him a big hug then would
feed him my lunch.
Your last sentence is also not grammatically correct. It should say:
If I ate my lunch, I would remain healthy.
This sentence also uses the past subjunctive mood. For verbs other than "to be," the past subjunctive mood happens to use all of the same words as the past indicative tense, so sometimes people mistake them. Make no mistake, though; in the above sentence, you "ate" is not the preterit, it is the subjunctive. Moreover, you can't properly insert "would" into the "if" clause of that sentence as you did.
Finally, you give the following example:
If I was going to...
"Was" is incorrect. Because the past subjunctive mood uses the same words as the preterit tense in all verbs except "to be," people often think that the past subjunctive of "to be" is the same as the preterit, but it's not. Where the preterit is "was," the past subjunctive is "were." The proper way to say the above hypothetical would be:
If I were going to...
Here is a link that explains using "was" instead of "were" when making a hypothetical conditional statement (a.k.a. second conditional) is incorrect: