To answer your second question, theoretically yes, the price is supposed to move up as the EPS will eventually increase owing to the lesser number of shares in the market (since bought back shares are cancelled, bringing down total number of outstanding shares, hence higher EPS)
I read this online ( Share buybacks and why they’re important to shareholders (santander.com)):
Share buybacks enable companies to generate additional shareholder value. Under regular market conditions, the portion of profits that a company uses to buy back shares has a positive effect on the share price.
The point above highlighted in bold is important. The current market conditions and perception of the company have a role to play. For example, after announcing a buyback, if the company’s future prospect aren’t that great, then it’s of no use doing a buyback, in such conditions the share price could fall. Paytm from my understanding was a classic case of distributing cash which was not so freely available, and the markets didn’t like it.
How do traders approach it? that I don’t know 
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