To answer the question of if a Permanent Member of the UN SC can use their power to veto an application for Member State, then the answer is yes, they can.
However, that said, since 1972 China has only used its Veto 9 times. And only 1 was regarding the admission of a new Member State. In this case, it was an application by Bangladesh, and occurred in 1972.*
To answer your other questions:
1.Doesn't China's veto power mean that it would most certainly veto any membership application by Taiwan to join the UN, and therefore it is impossible for Taiwan to join the UN?
Interestingly enough, it's not China (directly) blocking the applications. As it stands, the main roadblock to Taiwan becoming a permanent Member State isn't China's position on the Security Council, but rather the General Assembly itself.
The process of application to become a member state is described here.
A lot of Taiwan's applications have not made it to the UN SC, rather being rejected outright by the Secretary General under the context of the General Assembly resolution 2758, which recognises the PRC as "the only legitimate representative of China to the United Nations" and reinforces the UN's 1 China 'policy'.
This is a rather good article on it, and also answers your second sub-question:
2.Is there some viable alternative strategy for Taiwan to join the UN
Short answer is, at this stage, no. While they are trying to work with UN organisations, Taiwan is not likely to become a recognised Member State of the UN.
*Here is a full list of the UN SC vetos.