Hello, and greetings from inside a flat in Singapore in fact - I hope my first-hand experience with matters on the ground will come in helpful. To answer the questions directly:
1. For specifically high-floor buses, SBS Transit has the Royale bodied Olympians (
very few units remaining, will be down to 3 of them by October) and the 50 single-decker Volvo B10Ms. Both of them will be completely retired by 25 December, so it's basically your last chance to get them. On the SMRT side, there's the Mercedes-Benz O405G articulated buses with Hispano Habit or Volgren bodywork, however these are also beginning to be retired.
Other vehicles of interest might be the rest of the non-Wheelchair Accessible (but low floor) fleet; namely the 20 Dennis Tridents, 51 Volvo B10TLs and 12 Volvo B10BLE (CNG) buses, if you'd like more info give me a shout and I'll direct you as best as I can
I find the sgwiki website quite useful to check, specifically
https://sgwiki.com/wiki/Bus_Deployments and
https://sgwiki.com/wiki/De-registration_of_Buses which are as they state. Note that the deployments are not static and they sometimes rotate amongst services, but only within the same depot group.
To track down these older uses, a good app would be the Transitlink app which states whether the bus is wheelchair-accessible or not - an example would be over here:
http://i.imgur.com/i4Gn9rp.jpg this however does not give you any more details such as the exact type or registration which one might be used to in London, but I hope it's at least something.
2. Out of the 13 packages, two have been commenced, a third has been awarded and a fourth is currently in the process of tendering. The two are the Bulim Package operated by Tower Transit in the West and the Loyang Package operated by Go-Ahead in the East, while the Seletar Package has actually been won by SBS Transit and will commence in 2018.
As for the old SBS Transit livery, many of the buses by SBS Transit are currently still in their livery, doubt they've
repainted any of them into the green one although they do have some new units which are in the green colours. I doubt much will change by October, also the oldest units will probably not be repainted so at least that's something.
3. As for transport photography, experience states that you should be fine if you do it
outside the bus interchanges/termini themselves, most cases I know of people getting approached by security were doing it within the confines of the bus interchanges / termini itself; as far as I know the attitudes towards public transport enthusiasts in Singapore are a far cry from how it is in other places like Hong Kong for example. Of course there's no harm seeking prior permission from the relevant authorities before hand, I've never done it myself though so my experience there is limited.
As for specific places to snap, the exit of Hougang Central Interchange is a pretty common spot for standard, 45 degrees shots (and that's deep in SBS Transit territory so there should be a handful of their livery there). As for safety you should be fine almost anywhere you go, especially if you stick to areas around major transportation hubs, they're all bustling with people in my experience. If you're looking for something slightly more unique, let me know and I'll see if I can help.
4. Don't know much in terms of general advice, but the usual stuff; shopping down Orchard Road, seeing the Marina Bay Sands, spending a day on Sentosa Island (there's buses there too, lol), I'm definitely not an expert on those stuff though :P
Once again I hope this has been useful, if there's anything else you need to know, let me know and I'll see what I can do

and hope you enjoy your time here.