Most of the full nodes are operating on normal CPUs which is now basically ineffective for mining. The mining process is handled by specific mining pools. So for full nodes that basically sees the same blockchain (there might be inconsistencies at the tip if two blocks are mined at the same time), they have the same UTXO set. This is because the UTXO set is built based on the transactions that are included in the blocks. Whenever a block is received by a full node, they delete the UTXOs which were consumed by the inputs in the transactions and add the UTXOs that were created in the output. For a mining node it is similar. If they mined the last block at the same time as the other miner, then the first miner would be building the next block using a different UTXO set than the other miner. However, after one or two blocks when the network converges (they cannot indefinitely generate blocks simultaneously) the network would have the same UTXO set.
For mempool the story is different. Bitcoin transactions are relayed on the network on a best effort basis. So it might be the case that some nodes do not see some transactions until they are finally included in the blocks. So, yes there are inconsistencies in the mempool.
how can a node resume mining after the new block is introduced?
As mentioned above, if two blocks are mined at the same time then some miners would be working on a different version versus others. The accepted principle is to build on the block that was received first. However, this is not always the case. So when a mining node who is still calculating the header hashes notice that a new block is mined, they realize that they have lost the 'race' for that particular block height and try to mine on the block that was most recently received.