According to OALD, seaside - Definition and pronunciation | Oxford Advanced Learner's Dictionary at OxfordLearnersDictionaries.com

an area that is by the sea, especially one where people go for a day or a holiday/vacation

2. This is a seaside home. - Это дом на берегу (на побережье), but the context is that it's near the sea (i.e. берег моря), so Это дом на морском берегу (на морском побережье) are also OK.

(To Basil77, мой дом means the person OWNS it or LIVES there, but 'This is a seaside home' says nothing of the ownership or living there. You CAN use 'home' just to describe a дом. To quote Chicago Tribune, Understanding Different Types of Homes - chicagotribune.com)

A widely used phrase is 'seaside resort', in Russian it is морской курорт, or even курортный город (town near the sea).

So 'seaside' can translate differrently into Russian, but one has to express the idea that it is something in the vicinity of the sea, ocean, beach (as a rule, something man built such as road, home, hotel, resort, and usually in a vacation or leisure-like situation).
The possible translations are морской, прибрежный, на берегу, на побережье.

3. The seaside area. - Прибрежная территория, there are also technical terms like Прибрежная зона, Прибрежная полоса (zone, area, strip), or Курортная зона (vacation area, usually in a seaside situation).