Having visited both cities this July just gone, I can offer some advice. I also stayed at the Conrad Singapore. I have taken day trips to Kuala Lumpur, while I have also taken day trips to Singapore.

I would suggest staying in Singapore for the whole 3 nights.

To answer your questions:

1) In terms of weather, it is much the same year round.

2) The "usual" tourist haunts... Singapore Zoo, Singapore Botanic Gardens, The Original Singapore Walks, Pulau Ubin, Clarke Quay, Orchard Road. Definitely do some research on the best hawker centres. Check out sites such as TripAdvisor for more things to do.

3) A taxi from Changi to Conrad will cost around S$18.00 but of course will vary on time of day. The super efficient MRT will take you from Changi to Promenade MRT for S$1.74 with 2 transfers. A suitable option if you are travelling with minimal luggage (3 day trip?) and are travelling off-peak.

The Conrad was ok. Maybe my expectations too high or they didn't take me seriously as I was only 19.