HOW TO CONNECT CERTAIN VERSIONS
Remember to press the 'B' button on the 'stand by' screen to see 'connect', otherwise your Tamagotchis will not connect. Be sure to press the 'B' button on only one of the Tamagotchis, not both! Otherwise you will get an error.
Connecting a v2 to a v3 or v4 / v4.5
On the connecting options for the v2, select "Version 1"
On the connecting options for the v3 or v4, select "Other".
Connecting v2, v3, and v4 / v4.5 to the Keitai/Akai
On the v2, select "Version 1". On v3 and v4, select "Other".
On the Keitai / Akai select "Tamagotchi Plus" (symbolized with a + next to Japanese text).
Connecting v4 to v4.5
On the v4, select "ver. 4", and select what option you'd like to use (Game, Present, or Visit).
On the v4.5, select "ver. 4 / 4.5" and select what option you'd like to use (Game, Present, or Visit).
⇨ Connection v4 / v4.5 Connecting Glitch
For whatever reason, the v4 and v4.5 both are picky about connecting. Sometimes, when you try to connect them to any other Tamagotchi, they will just say "FAIL" instantly.
To correct this glitch, reset the v4 or v4.5, download your character, set the correct date and time, and try again.
Connecting Music Star (v6) to v5 / Famitama or v5 Celebrity (v5.5) / Royal Famitama
On the Music Star, select "Others" and wait on the Standby screen. DO NOT PRESS B.
On the v5, select the first option, then "Game", and then press B.
Marrying Music Star (v6) to v5 / Famitama or v5 Celebrity (v5.5) / Royal Famitama
After building up friendship levels on both toys to their highest possible levels, start the connecting process. But for the Family pet, select "Marry" and then "Give".
The adult will disappear from your Family toy, and appear on your Music Star as Nazotchi. You will receive an egg with the new baby, and Nazotchi will stay and live with your Music Star.
⇨ Music Star (v6) / v5 Marriage Glitch
Please be careful when marrying your v6 with the v5.
The Music Star will take about twice as long to build the friendship level than the v5. The Music Star's Friendship Meter consists of 8 stages: four static faces, and then four smiling faces. Be sure to have all four smiling faces before deciding to marry the v5.
If you don't do this properly, your Music Star will refuse to marry, but the v5 will accept - sending a character away and leaving you with one less character and no way of getting it back.
*Source: Tama-Zone (copied and slightly edited)