The hotel to the Ocean Park: you can walk to the Jordan MTR station to Admiralty MTR Station and then change to Bus 629 to the Ocean Park. Or take Bus 2 at Bathan Road to Tsim Sha Tsui Ferry terminal and take Tianxing ferry boat to Central, then change to Bus 629. The tram station to the Peal is just a few minutes from Central. So you can get to Central first and walk to the Peak.
No need to buy the tickets onling. Yes, you can buy octopus card for three days in Hong Kong. If you use it to take subways to get around the city and use it to pay for the single single or round trip airport express line, you can charge 200HKD into the card. You can get the change back and 50KHD deposit back, and pay 7HKD fee for refund within 3 months.