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If I browsing a tribe (e.g. PALNET) in Steempeak and comment on a post, will it use my SP in Steem, or my SP in PALNET??

Whether you browse a post or comment to a post, no matter what tribe it is , no matter which front end it is, it will not consume your voting power, so it will not use the SP. Only in an upvote, the SP is exercised in general. 

If you are voting a post in a Steem post and if the same post if tagged in palnet or tagged to any other tribe (such as steemleo or neoxianag) then all the powers will be exercised(SP, PAL Power, LEO Power, NEOXAG Power). If a Steem post is not tagged to other tribe then only SP will be utilized.

So to sum it up, for commenting to a post will not consume your SP. However as every activity requires some amount of resource credits, that will be consumed(but as you know, it does not have any monetary implication).