Some Google auto-suggestions for the search "do Aspies...."
There are no definitive answer for questions like these, because Aspies are individuals rather than some sort of hivemind. It's a bit like asking "do Queenslanders get jealous?" or "do redheads cry?" Some do, some don't, and it's hard to get any more specific than that.
But let's try...
1. Do Aspies feel love?
We can, yes. Successful romantic and family relationships don't always come easily to people on the spectrum because of the interpersonal shenanigans that come with the territory, but they can happen and they do happen. Sometimes that very difficulty means that when they do happen, they're cherished all the more.
But feeling love and expressing love are two different things. Sometimes we might struggle to identify and express what we feel, or express it in ways that the other parties can't interpret. Trouble with emotional expression, not liking physical contact for sensory reasons, or not being good at spontaneity can all make it hard to express the love we feel.
2. Do Aspies get jealous?
We can, yes. A particular source of jealousy can be people to whom social graces come naturally and who are gifted at interpersonal dealings. It can be really hard to watch someone do without thinking or effort something that you struggle with every day.
Romantically, I can see the case for an Aspie who's in a relationship being a jealous partner, worried that their social skills or ability to party can't compete with NT rivals for their beloved's affections. I can't say I've ever seen that scenario play out among the people on the spectrum I know, but it's not beyond the realms of the imagination. (BTW, a reason is not an excuse. Jealously at the point where it leads to things like creeping on your partner's email, giving them a hard time if a random stranger smiles at them, or trying to control who they see or talk to, is never OK regardless of your neurology.)
Then there's the question of when 'jealously' becomes indignation or outrage at very real injustices many people on the spectrum face. For instance, the workplace participation rate for people on the spectrum is just 34%, compared to the national rate of 83%. So a person on the spectrum who could work, wants to work, and is looking for work, but can't get a job (maybe they don't interview well, or have trouble networking) might well feel something akin to jealousy for people who've found work easily.
3. Do Aspies cry?
We have tear ducts and emotions and hormones like everyone else, so I guess so. Here come those differences in emotional expression again: some people on the spectrum have a 'flat effect', appearing to come across as unemotional or cold regardless of how they're actually feeling. Sometimes the things that press our emotional buttons are on the unusual side: things you'd expect to trigger gales of laughter or a flood of tears get nothing, while something an observer might think was quite trivial can cause a massive rush of emotion. Different things cause different emotions in different people.
4. Do Aspies lie?
Hells yes we can.