Can you take an alternate cardio event if on a temporary profile? Also, do you have to have a passing APFT in order to IST?

The answer to your question is FM 7-22 (Army Physical Readiness Training), Para A-38:
"Alternate aerobic events assess the cardio respiratory and muscular endurance of Soldiers with permanent medical profiles, or long-term temporary profiles that cannot perform the 2-mile run"

And...

Para A-41: " Soldiers with temporary physical profiles must take a regular three event APFT after the profile has expired. Soldiers with temporary profiles of long duration (more than three months) may take an alternate aerobic event as determined by the commander with input from health-care personnel. Once the profile has been lifted, the Soldier must be given twice the length of the profile (not to exceed 90 days) to train for the regular three event APFT. If a regularly scheduled APFT occurs during the profile period, the Soldier should be given a mandatory make-up date for the APFT."

For your second question, please define what IST stands for.

Yes you have to have a passing APFT unless the gaining state decides to waive the expired / failed APFT.

NGR 600-200 Section IV "Interstate Transfer" 4-13 (f)

f. Restrictions. Do not transfer Soldiers:
(1) Who do not meet medical retention standards. Waiver is not authorized.
(2) Who do not meet the standards of AR 600-9. Waiver may be authorized by the gaining state if the
Soldier is making satisfactory progress in the weight control program.
(3) Within four months of current ETS at time of request for transfer, unless they immediately reenlist or
extend their current enlistment on or before the effective date of the Interstate Transfer. Waiver is authorized.
(4) With nine or more unexcused absences within the preceding 12 months. Waiver is authorized.
(5) Who do not have a current APFT (within the last APFT cycle). Waiver may be authorized by the
gaining state.
(6) Who is enrolled or pending enrollment in the Army Substance Abuse Program (ASAP) per AR 600-85.

The first question has been answered already. The second question I haven’t been able to find an AR on it so far. However you have to do all the leg work for a IST, with that being said you have to find a readiness NCO that will give you a paragraph and line number. Typically they will not do this if you are not green across the board and if you have flags you can pretty much forget about an IST.