Hello, can I use a FPGA working with a PC, and "send" the part of the code I want to accelerate on the FPGA rather than on my laptop (Pentium). IF yes, what protocol should I choose? I am working on machine learning/image processing domain.

There are a couple of ways you can go here. The simplest is USB to serial, your laptop sees the FPGA as a serial device via a USB -> Serial adapter. This is easy and cheap, but you are limited to around 1Mbit/sec. If you don’t need huge bandwidth then go for that.
The second is to go via Ethernet. This depends on having a physical Ethernet port available on your FPGA board, and requires rather more complex configuration/code at either end. You need to design a protocol for communication between the two that breaks the data down into packets of information and reassemble it at the far end of the link. This does however get you up to about 1Gbit/sec, less if your laptop only supports WiFi or one end of the link only supports 100MBit Ethernet.

To accelerate any function or offload processing from your laptop (CPU), There should be low latency data transfer between laptop to FPGA and then FPGA needs to transfer the result of processing back to Laptop. In rack scale servers FPGA devices are mounted on PCIe bus which has sufficient bandwidth for this.
But if you want to try this on laptop you may need a very high speed bus comparable to speed of PCIe.
Best way is if you can run a mPCIe cable from your laptop mother board to FPGA, otherwise you may use USB 3.0 or something. Also FPGA should be powerful enough to support your usecase, otherwise it may become bottle neck for overall performance