Your best bet for information about luggage handling will be to ask the airline you will be checking in with.
UK transit visa
According to https://www.gov.uk/check-uk-visa:
Transiting without a visa
You might be eligible for ‘transit without visa’ if:
- you arrive and depart by air
- have a confirmed onward flight that leaves on the day you arrive or before midnight on the day after you arrive
- have the right documents for your destination (eg a visa for that country)
One of the following must also apply:
- you’re travelling to (or on part of a reasonable journey to) Australia, Canada, New Zealand or the USA and have a valid visa for that country
- [other items omitted]
Dubai transit visa:
According to http://www.uaeinteract.com/travel/visas.asp:
Transit passengers stopping at Dubai International Airport for a minimum of 8 hours are eligible for a 96-hour transit visa. A valid onward ticket is required
Passports or travel documents must be valid for at least three months.
Citizens of the following countries are not eligible for the 96-hour visa on arrival:
Somalia, Afghanistan, Iraq, Niger, and Yemen.
Transit visas for passengers arriving at Dubai and Abu Dhabi International Airports can be arranged by Emirates Airline and Etihad Airways for their passengers or by Marhaba Services for those travelling on other airlines. Marhaba Services Tel: 00971 4 2162657; 2164629