Second conditional in English- Correct usage?

There are different ways that the conditional can be used. I did not know the names for the different types of uses, but according to the first site, second conditional refers to imaginary or hypothetical conditions and the second one refers to things that happened in the past. These uses are different from the examples that you gave.

I don’t know these by “second conditional” as you do, but as common “if… then”:

If you liked the hotel, then ring the bell.
If you like the job, then apply for it.
[Please] forgive me if I was wrong. = If I was wrong, then [please] forgive me.

The ‘then’ can be implied (as it is in your examples), but it often sounds better when stated.

Since a clause beginning with “then” is a dependent clause, it’s separated from the rest of the sentence with a comma (as the two clauses in this sentence are separated – for the same reason).

>> If interested, apply for the job.

Is not a 2nd conditional structure at all; “interested” is a past participle adjective – the subject “you” and verb “are” have been subjected to ellipsis and the sentence is better understood to mean ”[i]f you are interested, apply for the job.”

The other examples aren’t 2nd conditionals, which is why you don’t understand them in light of the explanations given on the page you referenced.

The hypothetical/imaginary nature of the “conditional” indicate some kind of counterfactuality, that is to say that the subject under discussion is, in fact, not true or occurring at the moment of the utterance. Hence:

>> 0 conditional If you heat ice, it melts.
>> 1st conditional If you build it, they will come.
>> 2nd conditional If I were you, I’d (I would) think of grammar as patterns, not rules.
>> 3rd Conditional If you had been at home, you wouldn’t have missed my call.
>> Mixed conditional If you’d done as you’d been told, you wouldn’t have a broken leg.

Clearly, in each utterance, there is something unreal about each situation; i.e. we aren’t heating ice right now, but I’m passing on some observation about the properties of solid water, etc…

Neither of the other examples you give fit neatly into the categories outlined above (language is like that). For example:

>> If you had a good time with ABC hotel, ring the bell.

Is a mixed conditional – it seems to be a past 0 condition with a present result. The same may be said of ”[f]orgive me if I was wrong”.

I disagree with @CWOTUS that there’s any need for “then” in these sentences. They are not premises and conclusions. They are just subordinate clauses and main clauses. Technical writers often insert the “then” because it parallels the “if…then” structure in computer code, but there is no language-based requirement for its presence.

@englishgeek, It has been so long since I was in English that I have nothing to add about the question but welcome to Fluther! :o)