I'll try to address each of your questions in order. I'm wondering if we should create separate community topics for each as they are all relevant.
Listing Search Ranking
The overall effect on HA/VRBO search ranking is hard to measure. The placement in search and the exact search ranking algorithms are not shared with us, the same way that Googles search ranking algorithms are not public. Last year HomeAway moved from a subscription level system where more expensive subscriptions could boost search ranking to a "best match" algorithm. The transition from old to new style listing subscriptions is not complete and there are still some old listings that are finishing out their subscription. As time passes, "Best Match" and listing quality are more and more important for ranking high in search. Here are some resources about "Best Match" and listing quality:
HomeAway has stated explicitly that listings are treated equally so there should be no specific penalty for being integrated vs. not. Managing your listing using MyVR can help you with a number of tasks related to "Best Match" including calendar accuracy, response time (using automated and transactional emails), conversion reporting, and acceptance of online bookings. I'll speak to conversion credit/reporting in more depth below.
HA/VRBO conversion credit is given for any reservations in MyVR that were booked through HA/VRBO or that the source is set to HA/VRBO. Any inquiry in MyVR that converts to a reservation can have its source set to HA/VRBO, but should really only be those reservations where the lead was initiated at HA/VRBO. For example, if a renter calls the phone number on a HA/VRBO listing and books, the reservation would be entered into MyVR. The source of the new reservation set to HA/VRBO. MyVR will report that conversion back to HA/VRBO earning "offline" booking conversion credit with HA/VRBO.
As @Jenny-Oest mentioned, MyVR improved conversion credit reporting last year which, at least anecdotally, seems to have improved rankings system wide. The more conversions from your HomeAway listings on- and off-line the more likely a listing is to appear higher in renter searches. Without MyVR management, in order to earn credit for offline bookings, you'll need to enter these "offline" bookings into HomeAway by creating a manual reservation. This is one of the big time savers when using MyVR especially when you're marketing your property across more than two channels.
HomeAway listings are non refundable. Instead, if you have an existing listing, they can apply credit for the time left on your subscription towards a new listing. For example, if you have 3 months left on a Platinum listing subscription with Global bundle (which may have cost you $1K+), you could apply those 3 months towards a new annual subscription. The new, non level, subscriptions cost $399 through MyVR. The credit forward is 3 months or roughly $99.75 prorated on the new subscription. A new annual subscription would cost roughly $299.25 after applying the 3 month credit from the old subscription. Did you notice that it didn't matter how much the original subscription cost? Time is the only thing that matters on the old subscription.
Guest Email Access
HA/VRBO will have access to emails of guests that book or inquire through HA/VRBO, however other inquiries that are not related to HA/VRBO will not be reported to HA/VRBO unless the source is set to HA/VRBO. Candidly, I'm not sure if the email address is used from offline bookings or not. This is a good reason to only set the source to HA/VRBO if a reservation was truly initiated there.
Trying it out
We have 2 offerings for HomeAway. HomeAway for Owners (fewer than 5 listings) and HomeAway for Property Managers (5+ listings). It is difficult to move from one offering to another and each is technically implemented very differently. If you're planning on having 5 or more properties listed on HomeAway soon, my recommendation is to wait until you can take advantage of the Property Manager offering. This thread originated as a "can I keep my reviews" question which really only applies to the Owner offering.
If you think you'll have fewer than 5 listings for a while on HomeAway then I'd recommend getting HomeAway for Owners setup. If you decided that you wanted to go back to calendar-only management it will take some work in both cases, however I suspect it would be easier under the Property Manager offering.
I hope this helps. This might also trigger some more questions that we're happy to address here.