Boris Johnson's advice to the Queen to prorogue Parliament has certainly generated opposition, but I am curious whether that action will have any practical implications. If Parliament hasn't come to a satisfactory conclusion about Brexit in the last three years, will three weeks really make a difference? Moreover, it seems that the MPs would still be free to speak to one another about proposed legislation, which they could then introduce when Parliament reconvenes. Or does the prorogation introduce procedural obstacles to introducing new legislation once the Parliament reconvenes? (Is anything now that possible, that would have been possible beforehand?)
The government is responsible for negotiating the UK's exit from the EU (or cancelling it), so the idea Parliament could come to some kind of conclusion is really a distortion of the truth used by politicians trying to justify their actions. Parliament can only agree or reject a proposal that the government presents to it (a deal or no-deal), or pass a motion of no confidence in the government.
Parliament can however pass legislation to control the process of leaving the EU, such as by requiring the government to ask for an extension to avoid no-deal. The prorogation makes it harder to Parliament to do that. There is only 4 guaranteed days in September (starting from 03/09/2019, Parliament does not usually sit on Friday or weekends, and Tuesday the 10th is the earliest date for the start of prorogation) and perhaps 4-6 more in October for Parliament to pass legislation on this issue.
Note also that usually Parliament is not prorogued for the conference season, it is simply on recess. The crucial difference is that parliamentary services are still available, such as requesting documents and holding committees. Suspension also does not cancel any pending legislation that has not been completed, where as proroguing does. So if MPs fail to get legislation completed in September they can't finish it in October, they have to start from scratch only days away from brexit.
Yes. Part of what parliament have been doing is trying to force the Executive to not do what parliment doesn't want without actually letting them do anything. (I.e. Try to force an extension, meaningful vote etc, but voting against every single option of action.) This is probably due to the fact a significant proportion of parliament just want the blame to devolve on someone else. A course of action which forced them to 'put up or shut up' is bad for this group in particular, and since the result for many of the prevaricaters would be 'shut up' a side effect is that it's also bad for those MPs who actively seek a different solution to the one the executive is persuing.
Any parliamentary action on the Brexit process has to go through the legislative process. The representative of the UK for the Brexit process is the government. When the government is toppled through a vote of distrust, any elections for a new government will happen after the Brexit date.
Now there are three possible solutions for the EU/UK customs border which have to follow a Brexit:
a) None until something better has been developed and implemented. That's the backstop.
b) The Irish Sea. That solution was proposed by EU and accepted by May but rejected by the DUP as it would move Northern Ireland closer to Ireland.
c) The inner-Irish border. It would be a violation of the Good Friday treaty and likely cause renewed unrests. Nobody wants that but it would be the obvious consequence of the No Deal Brexit. Johnson claims that he wants to use the threat of a No Deal for forcing the EU to accept a different deal.
Now assuming that Johnson is talking the truth when wanting to use the very little remaining time to enact a different deal with the EU, the only actual way to do so is option b). Since it would throw the DUP under the bus, Johnson has to make sure that he'll keep his mandate for finishing the Brexit process even when the government breaks apart.
Prorogueing the parliament until it cannot stop Johnson from concluding the Brexit process would make sure that Johnson has the ability to tell the EU "it's either this previous deal you agreed to or a No Deal Brexit" and get this under wraps either way. Whether or not the EU agrees to stomp over parliament and the current government coalition, he will likely have a strong standing for his next election.
Of course this theory could also explain why nobody in the EU has so far heard of any proposal by Johnson: he needs to be in a situation where he can no longer be stopped even by the DUP before making such a pitch.
Prorogueing parliament will indeed give him, as he claims, the time to negotiate such a government-breaking deal and, more importantly, implement it because there would not be time or opportunity to stop it. When the EU clearly has only the options to accept what they had previously proposed themselves or no deal at all, there will be some likelihood that they decide for the former as the lesser evil.