This is gonna be a bit lengthy...

For bonuses you get from Wireless (aka Spotpass), there's a few stuff.

The most obvious one are the characters, they're all from the previous Fire Emblem games. The characters doesn't really have much purpose other than summoning them into the world map, in which you can fight them (to recruit the leader), or just pay with gold to recruit them. You could also buy weapons from them (some of which you may not be able to get easily until you've played further chapters). After buying stuff from them, or dismissing them, or defeating/recruiting them, they disappear from the world map, but you can still make them reappear on the map. Whether you wanna summon them it's optional.

Also, the benefits of these characters is that they can reclass to any type of class that they can access to of their gender (like the your Avatar). Only downside is they can't support, or get benefits of supporting and pairing up.

Next up is the Bonus Items, these are legendary weapons which are hard to get in the game unless you bought the Infinite Regalia DLC. They will be added into your convoy when you select them, but you can have only one of each of the weapons available in the DLC, so use them wisely.

The we have the bonus maps. Unlocking them will make them appear on the world map. You can only access them when you're at the last chapter of the game (aka Endgame). Without spoiling much, each map allows you to recruit a character.

Lastly, there are challenges, in the form of Double Duels. They are Local Co-Op Play only unfortunately.

Overall, these bonus stuff from wireless are optional stuff that may or may not make playing the game more fun.

Hope that answers your questions.

Marrying female avatar (aka FeMU) to Chrom is a really good idea.

Not counting FeMU, Chrom's best pairings from best to worst are:
Olivia, Sumia, Maribelle, and Sully.

So Sumia is also pretty good when paired with Chrom, just that if you choose not to pair her up with Chrom, she has very limited marriage options (aside from Chrom and MaleMU, she can only marry Frederick, Gaius, and Henry).

I guess its up to you since it's quite hard for me to answer that question, seeing that both options have some pros and cons.

Also, I think the reason why Chrom and Sumia has very limited pairing options is because their marriage is canonical. If you look at the intro of the game, you can see Chrom and Sumia holding their first child at one point

Yup. Useful for getting all the skills you want to make your perfect team. However, grinding too much makes all your units incredibly powerful and making the main story cakewalk (like I did in one of my earlier play through of the game, where my team was so powerful one member alone was enough to solo the final mission).

stats have cap, and switching class too many times will end up your char getting max 8 exp per kills

Galeforce is one thing. Armsthrift and 50 luck your sorcerer and maximise his weapon for the win!

1 skill per parent

Lucina's skill from the mom is the skill at the last slot before end of Chapter 13. If the last skill she learnt was Galeforce, then Lucy gets Galeforce. Doesn't matter what class she is. Also, you can use the 'Equip Skill' option, to swap around to get the skill you want to be the last skill of your mom so Lucina has that skill.

For other child characters, the skills they inherit are the skills of their parents on their last skill slot. So if Vaike's last skill slot has Counter, then his son has Counter.

Lets say Sumia learnt another skill, like Rally Speed, but you want her daughter to have Galeforce (which Sumia learn already, but not in the last slot), use the 'Equip Skill' to move those two skills around to get Galeforce in your last slot, and her daughter will inherit that skill when you enter the Paralogue.

Also, each parent gives 1 skill to the child.

I have just confirmed it a while ago. The skills that the children get are the skills from the parent's last skill slot before entering the paralogue (not during battle preparation of the paralogue). During the paralogue, the children will already inherit the skills, which is a plus, since they're underleveled in the mission.

I used to think that the children will inherit the last skill the parents learn during before marriage, lol.