I would say yes to the new modem/router to be able to handle the increase in speed modem/router connected to PC by cable everything else is connected by WiFi to modem/router.
no, its like this.http://www.ebay.co.uk/itm/CABLE-2m-FOR-VIRGIN-MEDIA-TV-BROADBAND-TIVO-TV-WHITE-NEW-/251032337136?_trksid=p2385738.m2548.l4275
APPROVED MODEM SPECIFICATIONSRecommends customers purchase a cable modem that meets the following requirements for the best experience:DOCSIS 3.0 certified modem that has 24 channels down and 8 channels up (24x8) or higher.As an alternative, you may purchase a modem with these minimum requirements based on speed: If your speed is less than 200Mbps get at least a DOCSIS 3.0 (8x4) If your speed is 200Mbps through 400Mbps get at least a DOCSIS 3.0 (16x4) MINIMUM MODEM REQUIREMENTSDoes not currently support customer-owned DOCSIS 3.1 modems. EURODOCSIS cable modems are not supported in the United States