I think something that needs to be noted is the context in which an amphibious assault would occur, i.e. in what situation could the PLA use this option, and what state the Taiwanese military would have to be in for them to pull it off. As we all know military structure is generally linked together - it would be highly unlikely for Taiwan's Air Force to be decimated while leaving ground forces intact - command structures and coordination would very likely be disrupted to a considerable degree if the Chinese are able to launch a successful amphibious invasion.
Granted this does not change the individual specifications of the weapon systems themselves, just something to consider when hypothesizing combat scenarios.
On points one and two I am not as well-versed so I'll leave this to someone who has the expertise to answer it... I can only speak from experience in Taiwan, somewhat related to three.
I'm not sure how to counter the Javelin so I'm just tossing my weight around other factors that might influence Chinese tank use and their mission profile. I really don't have any answer as to a counter so I will consider the feasibility of the PLA using tanks.
To put it simply, Taiwan is a very poor environment for tank use, I personally have a hard time envisioning a situation in which the Chinese would have to use tanks in order to accomplish their mission goals, though it is certainly possible that I may have simply overlooked a mission. Taiwanese armor have consistently been faced with logistical problems, namely getting armor where it is needed - and this problem would be the same for any tank force, invading or defending. There are very few large plains on the western coast - most of it consists of urban areas and farmland (to broadly generalize). Tanks would most likely be used in the city, where it's questionable how the ground would be able to support the weight.
If someone can bring up a scenario where tanks would be absolutely imperative by all means bring it up.