No, you have them mixed around a little. 3 was the one with the Fire Bringer. 5 had the Sun Rune.
Definitely second this. Trails (Kiseki) is outstanding on every front, I have the Sky series on GOG, but still trying to get Cold Steel.
Wasn't Suikoden 4 the one with the Rune of Punishment? But anyway, I can see what you are talking about. Suikoden can be a daunting series at times, but it is so worth it. That's why I am backing the spiritual successor on Kickstarter, Eiyuden Chronicle.
Ooh... Boy! Where to start:
To start, I can personally recommend 0 A.D. (Open Source RTS) and Battle for Wesnoth (Open Source TBT), which I install on just about everything. Also, I recommend Sonic Robo Blast 2 and SRB2Kart if you have any fondness at all for 3D Sonic the Hedgehog games or kart racers. If you are a fan of classic Sid Meier's Civilization, then Freeciv is the best Open Source TBS out there. If you like rhythm games at all, StepMania is a great Open Source alternative. There is also osu!, which went Open Source in 2014. SuperTuxKart is another great Open Source kart racer.
If you are interested in Open Source remakes of propriety games that will require some files from the game in question then you can get no better than the Open Source remakes of Morrowind (OpenMW), classic Command & Conquer (OpenRA), classic X-Com (OpenXcom), classic Doom (ZDoom), and the Build Engine games like Duke Nukem or classic Shadow Warrior (EDuke32).
I'll just throw in the Suikoden series. I got into Suikoden with S5 on the PS2 and just went backward from there. Played every game except for 4 and Suikoden Tactics, though I have read LPs of both. Absolutely outstanding series in terms of both story and gameplay.
No arguments there. I would love to see anthology releases for each of the arcs: Sky, Crossbell, and Cold Steel.