The sea is home to all the decomposers in the world, which produce acid to carry out their task. Because of this, acid rain is more than common. In this world scenario, how could plants, animals and life in general be? What details could be added?
It would be very weird. Corpses wouldn't rot, trees wouldn't rot. to name a few consequences: Forest fires would become very deadly since trees don't decompose, so fires would burn many, many more trees, and have much more fuel. They would be harder to stop.
Bodies won't decompose
This would have many negative consequences:
People could hide bodies in any place where people won't look, and they don't have to worry about the smell giving them away. You wouldn't be able to use tracking dogs to find the bodies for the same reason.
People would save their dead bodies. If you are still attached to a dead relative, keep their body in a closet! If you have a celebrity who died, put his body on display! This would be very weird, although in your society it could be normal...
I don't have time right now to write a full answer, so hopefully, this will suffice. I will hopefully edit it in a few hours...
I'm going to make a frame challenge here:
What exactly separates a decomposer from a micro-organism that simply needs to eat something?
Without decomposers on land, you would not need a fridge since food would not decay. But food is food and if there are micro-organisms they are going to want to consume that food thereby decomposing it. The conclusion is that if there are no decomposers on land, then there are literally no micro-organisms on land. With no micro-organisms on land, the cycle of life on land would collapse altogether.
So I guess it could work as long as you're willing to have zero life on land, in which case acid rain wouldn't matter because the ocean is already full of the acid.
There was an era during which trees would mostly not decompose. It was the Carboniferous. The wikipedia article for it says:
The large coal deposits of the Carboniferous may owe their existence primarily to two factors. The first of these is the appearance of wood tissue and bark-bearing trees. The evolution of the wood fiber lignin and the bark-sealing, waxy substance suberin variously opposed decay organisms so effectively that dead materials accumulated long enough to fossilise on a large scale. (...) Based on a genetic analysis of mushroom fungi, it was proposed that large quantities of wood were buried during this period because animals and decomposing bacteria and fungi had not yet evolved enzymes that could effectively digest the resistant phenolic lignin polymers and waxy suberin polymers. (...)
The Carboniferous trees made extensive use of lignin. They had bark to wood ratios of 8 to 1, and even as high as 20 to 1. This compares to modern values less than 1 to 4. This bark, which must have been used as support as well as protection, probably had 38% to 58% lignin. Lignin is insoluble, too large to pass through cell walls, too heterogeneous for specific enzymes, and toxic, so that few organisms other than Basidiomycetes fungi can degrade it. To oxidize it requires an atmosphere of greater than 5% oxygen, or compounds such as peroxides. It can linger in soil for thousands of years and its toxic breakdown products inhibit decay of other substances. One possible reason for its high percentages in plants at that time was to provide protection from insects in a world containing very effective insect herbivores (but nothing remotely as effective as modern plant eating insects) and probably many fewer protective toxins produced naturally by plants than exist today. As a result, undegraded carbon built up, resulting in the extensive burial of biologically fixed carbon, leading to an increase in oxygen levels in the atmosphere; estimates place the peak oxygen content as high as 35%, as compared to 21% today. This oxygen level may have increased wildfire activity.
So I don't know about acid rain and decomposition only in the seas, but trees would grow on top of each others' dead trunks because those would never rot; The soil was acid, wild fires were much more common than today and cockroaches were bigger than your foot. All in all a worse scenario than you proposed, yet life thrived. So I think life would be ok in your world too.