Regarding speech - I was reading an article recently about some research in this area. Scientists divided kids who didn't speak and were about 2-3yo in three groups.
All groups had a class where teacher would show cards with animals and say something like "Dog, dog says woof-woof"
1st group had no physical trainings and was a control group
2nd group had physical training to train gross motor skills
3rd group had physical training to train fine motor skills
Results were following:
1st group no progress
2nd group kids were starting to imitate sounds
3rd group was the best in progress, kids were trying to pronounce words and had some success in it.
Scientist explained that areas responsible for speech and fine motor skills are close to each other, so triggering motor skills helps to develop speech.
Remember all that baby games where moms/dads are doing some tricks with fingers and teach kids to do so? itsy bitsy spider for example. It all helps.
Besides talking to the kid showing him things and naming them, voicing all actions you and your kid do, so his vocabulary will be expanded as much as possible.
And kid should feel that gestures doesn't help parents to understand him. You can say: " I don't understand what you want. Just tell me. Do you want this? Or that? Look daddy says " give me milk" and I give him milk, now your turn" Pretend that you don't understand, he may realize he needs to learn to speak.
Regarding tantrums and refusing to walk - of course its better to sit and be carried then walk :) I'd love to do so too :) Force him. Say mommy/daddy is tired. Look all boys and girls are walking by their-selves.
Tantrums are hard to handle, try to discract him with toys or game, but don't pick him up. Don't do what he wants, but do everything else to distract him/calm him down.
Everything that you described is not a sign of any development issue, I've seen kids who were not talking until 4-5yo. Usually boys are the lazy ones, they don't do things if they think they don't need it.
You just need to spend some time to help him in his development. And explain that tantrums won't give him what he wants. But simple words will.