First, yes, 〜ないといけない is a grammatical phrase, usually translated as "must" or "have to". Correspondingly, it will usually be written in hiragana rather than kanji.
Second, your confusion is totally natural; I think a lot of Japanese learners will come across constructions with a couple of negatives and a conditional in the mix and wonder how to parse it... ...
-ないと doesn't indicate "must", but -ないといけない does (the 行 also usually wouldn't be written in kanji in this case, either). It's one of a few set phrases that just mean "must", and are pretty automatic when that's what you want to express. Some similar patterns that work the same way are:
Instead of using -ないと, you can also use -なければ or -...
くれりゃ is a colloquial, contracted pronunciation of くれれば.
For this kind of contraction, see this thread:
What is the meaning of りゃ in this phrase?
注文してくれれば breaks down to...
注文して -- "order", the て-form of the する-verb 「注文する」
くれれば* -- "if you do ~~ (for me)", the conditional form of the subsidiary verb 「くれる」
(*ば is a conjunctive particle)
For more ...
They are not equivalent. The difference between the two is that of ability vs. permission. In English, both of these concepts can be expressed using "can", which is the reason why Google Translate offers the same result here. So these two sentences actually mean:
(1) Am I able to pay by card?
(2) Am I allowed to pay by card? / May I pay by card?
The nuance of this きっと言うかな is somewhere between "I believe he will say" or "I guess he will say".
The meaning of きっと is close to "I believe" rather than "definitely". It's a relatively subjective expression and the statement does not have to be based on an evidence. Using "definitely" to translate きっと is too strong in many cases.
かな is both "I wonder/doubt"...
am i able to pay with a credit card (at this store)?
may i pay with a credit card (at this store)?
I agree with Kaskade's comment. Ability vs Permission. In the case of the credit card example, you are able to use 払うことができますか because the store may not be physically able to process your credit card (lack of a credit card ...