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Is there a way to make FPGA read and write to RAM on PC via PCI interface?
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The Cyclone IV GX Transceiver Starter Kit uses a PCI Express rather than PCI bus interface. Both are almost software compatible in the higher protocol layers. A PCIe or PCI bus device can basically access memory through DMA. This is mainly a problem of required programming at the PC side. I don't know, if Jungo WinDriver used in the Altera reference design provides DMA capability. In any case, it'a an advanced PCIe driver topic and not suggested for a first project.
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I am also wondering how to make FPGA access its internal memory.
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Do you mean FPGA internal RAM or SSRAM of the starter kit? There should be Altera examples for both.