can opendns increase my internet connection speed?

For me it is true. Because with my ISP the OpenDNS worked perfectly. Accepted ok the dns service and the speed of the connection really speeded up. In navigation of sites, in downloads, in stream of videos, in everything, and the better, the OpenDNS helped me too much to stop with my network problems of dns.

It depends of the DNS servers of your ISP : you need to try. If your ISP uses reliable DNS servers, you will probably get better results by modifying the behavior of your browser DNS caching. By example, for Firefox, increasing (about:config) the value of Network.dnsCacheExpiration to 3600 (1 hour) and of Network.dnsCacheEntries to 1000 (by default, it's only 20) boosts really the performance. But this give dns errors sometimes ; you can manage them with an add-on called DNS Cache.