I think you are over-analyzing. would like with an infinitive is an idiom expressing desire. would love is an emphatic form of would like .
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AnonymousIf you have a pen, I would like (want?) to have it please. -- IMO, first conditionalNot every sentence with if can be classified as first, second, or third conditional. I think your first sentence falls into this category. It's simply not classifiable withi
If you had a pen, would I be able (could) to have it? -- IMO, second conditional