I think they are completely interchangeable when talking about a store where you can buy things. Some people may prefer one to the other but there is no real difference.
But "üzlet" has a wider meaning in business. A business deal is an "üzlet". Occasionally a small barter transaction is also called a "bolt" but anything more serious is an "üzlet". "Üzlet" is more official, more professional. And Business, with a capital b, is "üzleti élet" - "business life". Businessman is "üzletember", a trader is "üzletkötő", etc.
But I can still open a small store on the corner and call it either a "bolt" or an "üzlet".
Note, "üzlet", in this sense, if definitely an actual, physical store where you can walk in and buy things. Do not use it to describe just any business, any company, as in "small business". An üzlet is a place where you can shop.
"Üzlet" can also be a small place where you buy a service, like a barber shop, a hairdresser's, a shoe repair place. You don't use "bolt" for these.
You can ask "how is business?" - "hogy megy az üzlet?", and it can mean any company, although usually it means a store. You can also ask "hogy megy a bolt?", and that would be more restricted to an actual shop, not just any business.
Not really. Jewelry shop can be either ékszerüzlet or ékszerbolt, butcher's store is almost never "hentesbolt" but "hentesüzlet". There are many other examples a tobacco store sounds a bit strange as "dohányüzlet" as that is more often "dohánybolt" (but the most popular name is "trafik"—Hungarian truck drivers call the Turkish traffic police (when they have "Polis trafik" written on the car) "lengyel dohányboltosok" (polish tobbacoists). I don't think it could have any connection to smokey bears or other American nicknames for cops... In general, if we use "bolt" we usually refer to a small place, while "üzlet" is not necessarily but usually a bit bigger. Sounding may also has influence to this.
Okay, the difference is sublime but crucial. "Elöl" (with dieresis or umlaut) is on the first place of something" or "on the front of something" or "at the front end" or "forward" but as the part of the thing. Let's say, the driver is on the front end of the bus" - "a vezető elöl van a buszon". "The driver in pole position sits in front of the pack" - "A pole pozícióban lévő vezető ül a mezőny elején".
"Előtt" is very similar but the something there is not part of the others. "The famous 'Tank Man' stood alone in front of the tanks" - "A híres 'Tank Man' egyedül állt a tankok előtt." Also note that "előtt" often refers to time. "Karácsony előtt jártam a Holdon" - "I walked on the Moon before Christmas".
There is a third one to make your job even more interesting: "elől" (with double acute) means from something, like escaping or running away. "Elfut a tank elől (aki nem Tank Man)" - "Runs away from the tank (who is not the Tank Man)" or "elmenekül a tűzvész elől" - "escapes from the wildfire". It is also used for movement that leads away from a certain point: "Állj el az ajtó elől, kérlek! - "step away from the doorway please".
I hope I could give you a practical help ;)
Definitely no. You may accidentally see this but it is a rare and obsolety abbreviated form of [the guy] who stands in front of the store. The common form should be [A fickó] aki az üzlet előtt áll and here the "aki" (or "ki" in its obsolete, abbreviated form) is a referrer, actually a relative pronoun.
(Please note that "guy" and "fickó" is very colloquial, almost slang. You'd better not to use it but you'd better understand it ;) Also "guy" has many possible translation with slightly different overtones. "Fickó" is one of the more acceptable form. If you tell a police officer that "that guy gave me this ticket" az a fickó adta ezt a jegyet [e.g. when you got fake entry ticket to Sziget Fesztivál] it would be as acceptable as in American English.)
Duo, please offer an option of slow-speed pronunciation! Beginners need to develop an "ear" for hearing the 44 totally different alphabetic pronunciations. It would be so helpful if Duo would offer Beginners a drill, repetitive, focused on pronunciation, to support their listening skills.