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Is obtaining an EEA family permit enough to be granted an entry to the UK?
No. You also need a valid passport, and your spouse must be in the UK already or arriving with you.
Does EEA family permit automatically give me the right to work?
No. Your right to work flows directly from law, in light of your relationship with an EEA national. Unfortunately, if an employer asks you to prove your right to work, they're unlikely to accept the EEA family permit, because it is not on the list of approved documents. But if they don't ask you to prove your right to work, you can work, as long as you are with your spouse in the UK.
Questions about moving for a long time, for example, to work, are off topic here. If that is your intention, and you want more information, you should ask at Expatriates.