if we cultivate automatic plants outdoors, can the rain damage the plants

Not directly, but having wet buds can lead to bud rot, particularly if it's raining often. You also don't want the plants wallowing in super-wet ground that never dries out, as this is basically over-watering. I would recommend creating some kind of shelter for them - a polytunnel can be made very cheap and inexpensively using bamboo canes/PVC pipes and a roll of polythene - so you can prevent water from getting onto your maturing buds and control the watering cycle a little more as well. If you have a greenhouse, even better!

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too much is a problem... overly moist will increase risk of bud rot and other infections. Too much weight can cause physical damage to the plant. 2 summers ago i tried an outdoor grow in my backyard... not enough light, but that's a different story.. anyway, august and september were humid and rained often... i ende dup haveing to cut off some colas with initial infection of bud rot... So, just inspect them well... If it's raining constantly, a fan on them after it ceases can help evaporate that water faster... outdoor fans that are powerful like that are very expensive, though. but, anything that reduced length of time they are wet will help... and wouldn't worry unless it's happening at an unusual frequency.

If its heavy enough you might get a broken branch or some but most of the time they love the rain

Very, very unlikely. But, rain could cause indirect damage, such as a storm dropping a branch on your plant or your plant getting flooded out due to poor soil.

The rain wouldn't hurt them. You'd have the same issues as growing photos outdoors.

Damage not, but a lot of humidity for some time will cause mold in the buds, if it is already flowering