Yes. Absolutely.
Dialects are not inherently location based. They're simply varieties of speech that are shared among a group. We often think of them as being based on location (a.k.a. topolect or regiolect), but they can also be based on gender, socio-economic distinctions (sociolect), or age. "Dialect" is just a general term referring to a variety of speech, and the concept itself doesn't actually have any inherent relation to geography. It's just the most common way the word is used among the general public.
There's a definition of dialect that works well here. It also addresses the language/dialect distinction, and since there's a good chance that gets brought up, I'll post this in full:
A variety is any body of human speech patterns which is sufficiently homogeneous to be analyzed by available techniques of synchronic description and which has a sufficiently large repertory with broad enough semantic scope to function in all normal contexts of communication.
A language consists of all varieties which share a single super-posed variety having substantial similarity in phonology and grammar with the included varieties of which are mutually intelligible or are connected by a series of mutually intelligible varieties.
A dialect is any set of one or more varieties of a language which share at least sone feature or combination of features setting them apart from other varieties of the language, and which may appropriately be treated as a unit on linguistic or non-linguistic grounds.
In my specialty, generational dialect differences are just as important to address as regional ones. If you're looking at any scholarly work on Sinitic dialectology, you're likely going to see generational dialects brought up, marked as "old" or "new", and in some cases you'll also see an intermediate dialect given. In those cases, new refers to how 20-somethings are speaking. Old is usually their grandparents' generation.
Yeah, this can certainly happen.
One of the classic studies involving generational language variation is William Labov's 1963 paper "The Social Motivation of a Sound Change," which studied variation in the vowels /aw/ (like in "house") and /aj/ (like in "eye") on the island of Martha's Vineyard, Massachusetts.
The dialect of Martha's Vineyard natives tends to "centralize" the pronunciation of those vowels. This means that when those vowels are articulated, the tongue doesn't move as far from its neutral position in the center of the mouth, compared to its position in other American English dialects. While this feature of the dialect was present in speakers of all age groups, Labov found that the tendency was much more pronounced among younger natives of the island, particularly young men involved in the fishing industry.
His conclusion was that these younger speakers were emphasizing this characteristic of the Martha's Vineyard dialect in their speech to assert their identity as natives of the island, and to distinguish themselves from the increasingly common "summer people," meaning temporary residents or vacationers.
(By the way -- since this is really more of a linguistics question than a history question, you should try asking at /r/asklinguistics too. I'm sure the folks there will have helpful answers.)