Water Coming Into the Fireplace
This usually indicates that the flashing around the chimney is bad or the cap may need to be repaired or replaced. It is also possible that there is an issue with the brick or mortar of the chimney itself. In any case, it's best to call a chimney and/or roofing contractor to inspect and complete the repairs.
Smoke Entering Room
First, check to make sure your flu is open. If it is, you may have some drafting issues in your chimney. This has quite a few possible causes, most of which should be addressed by a chimney professional. Have a chimney pro come inspect your chimney and fireplace and diagnose the problem. Do not use your fireplace in the meantime. Using a fireplace with draft issues or other problems is a serious fire hazard.
Animals entering the fireplace
It isn't uncommon for critters to find their way into homes wherever they can, and chimneys are a great access spot for them. Squirrels and bats are especially adept at entering through small gaps. Animals can do serious damage to your home and they can be a health hazard too. If they are entering through your fireplace, there is a good chance your chimney cap needs to be replaced. If you have a brick or stone chimney, there may be some damaged brick, stone, or mortar areas where they are entering. You'll need to address both the critter removal and the chimney repairs to fix the issue. Call experts in each field to come diagnose the problem and make any necessary repairs.