1st Qn: No.
2nd Qn: It'll cost you $1.90 plus the unrebated fare of the last
trip, provided the first 4 trips meet the criteria of a "journey"
(read below).
To clarify this interesting point (this is, of cos, interesting to
any bus spotter who is not on a bus pass!), let's see an excerpt of
the latest definition (not that it has changed) of the Unlimited
Bus Transfers system from the recent Bus Fare Amendment
notice:
"Continue to enjoy unlimited bus transfers for a
journey at only $1.90... We guarantee a maximum
fare of $1.90 on our basic bus services when using the ez-link
card."
The keyword here is a journey, which is up to 4 bus trips
that all meet the eligibility criteria for transfer
rebate:
1. From MRT/LRT to bus, bus to bus, or bus to MRT/LRT, you must
transfer to the next service within 45 minutes of
exit from MRT/LRT gate or from tapping the card on the bus
exit card-reader.
2. NOT RELEVANT BUT
INCLUDED: For all concessionary travel on buses or trains, the time
allowed for the next transfer will also be 45 minutes of exit from
MRT/LRT gate or from tapping the card on the bus exit
card-reader.
3. The first, second and third valid transfers on a journey must be
made within 2 hours of the first boarding on the same
journey.
For the third point, in a gist, it means you must board the 4th trip within 2 hours from the time
you board the 1st trip to qualify for Bus Fare Cap and each
alight-to-board transfer should not take more than 45
minutes.
Now you know there's no such thing as unlimited bus transfers for
the whole day, but you have to take these buses in a string.