Learn English – the feminine equivalent of “guy”

Mental hospital (which, as you say, corresponds to ospedale psichiatrico) is a reasonable choice for the lunatic asylum sense of manicomio. Psychiatric hospital or psychiatric ward also are reasonable. In some instances, rehab and retreat may apply. Loony bin might also apply but has an entirely different tone.

I don't know of any terms that deliver specifically what you've requested. You might consider:

• Infatuation. No age implications, has a sense of obsessiveness.
• Crush (noun def. 2). Informal. Has some sense of childishness and is also transient or brief.
• Passing fancy. Not nearly as strong as love, no age connotations, short lived. However, the phrase is a bit antiquated sounding (to my ear, at least), so it might be appropriate for describing the elderly.
• Smitten (adjective). Includes those genuinely in love, no age connotations. Someone smitten, especially an older person (who we generally assume has experience and isn't as susceptible to powerful feelings as a teenager) has fallen in love hard and fast and has at least some of the characteristics of someone infatuated, though there's at least an equal chance they're "really" in love.

Honestly, it's quite acceptable to use puppy love the way you want, as long as you give enough context to make it clear who's experiencing the feeling. Though it's most commonly used with youth, the definition isn't restricted to them. Describing an elderly person or couple with it even gives the phrase some extra weight, by implying they were so stricken that they behaved as if they were teenagers again.