Welcome! The issues you described are typical of an older car. My 2004 Acord Euro has similar issues. For your shuddery automatic, first thing is to replace the transmission fluid with Honda ATF. The second problem can be resolved by replacing the powersteering fluid, and checking the accessory belt tensioner. If the tensioner shows that the belt is worn (triangle pointing at the smaller square, instead of the tall rectangle), then you need to replace the accessory belt. It is a 7PK1750.
Vibrations through the steering wheel at idle is typical, it means your engine mounts are worn and need replacing. I just did mine, you need the front and rear hydraulic mounts, the left and right mounts, plus the subframe mounts. Not an easy DIY, better to get the parts and pay a mechanic to replace them.
Brakes will need new brake fluid. Not just by bleeding through the calipers, but possibly, pushing the pistons back in while bleeding at the same time. Mine came out black in colour, eventhough I religiously flush brake fluid from the master cylinder reservoir to the brake caliper bleeders every 2 years.
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