If a feature gives proficiency in a skill you are proficient with, can you always choose any skill to replace that proficiency?

Page 125 of the PHB has this statement:

If a character would gain the same proficiency from two different sources, he or she can choose a different proficiency of the same kind (skill or tool) instead.

This statement is given in the context of character creation, and specifically skill proficiencies given by backgrounds.

Does this rule apply to any feature gained at any level that gives proficiencies, or only at first level?

Language proficiency per week of downtime

One of my players does not speak common as they come from a village the speaks entirely elvish. We are coming up on a couple weeks of downtime in the campaign and another one of the players wants to teach them common. According to the Xanthar’s rules it takes 10 weeks to become proficient in a language, but they would learn some over a couple weeks. My question is how much of a language would a character pick up in that time span? How would they role play speaking common with a limited knowledge?

Where has my History proficiency come from?

I’m new to DnD. I was typing up my character sheet (I’ve decided to do this every now and then as my annotations become more messy), and in the process I didn’t spot any reason for me to have the History proficiency I have.

It’s likely that I just made a mistake when making the sheet, but maybe I didn’t…

I’m a Dragonborn Paladin with an Outlander background and my subclass (Oath) is Redemption. According to this wiki, the race or subclass doesn’t give me any skill proficiency, while the background gives me Athletics & Survival and the class gives me a choice of two from Athletics, Insight, Intimidation, Medicine, Persuasion & Religion; I chose Medicine & Persuasion. So the 4 skills I have from my background and class are Athletics, Survival, Medicine & Persuasion… none of those are History (which I have in addition).

I also noticed an “origin” feature for my background, from which there are 10 origins: Forester, Trapper, Homesteader, Guide, Exile or outcast, Bounty hunter, Pilgrim, Tribal nomad, Hunter-gatherer, and Tribal marauder. The wiki doesn’t give any information on those, and I haven’t got one written on my sheet.

I’m currently Level 4; I don’t believe a level feature has given me an extra skill proficiency so far.

Where might I be getting this proficiency from?
Does my “origin” have anything to do with it?
What are the possible ways of getting a History proficiency?
Have I/my DM simply make a mistake when creating my character?

Does hurling a thrown weapon change the weapon’s category for determining proficiency?

On Weapon Categories says, “A melee weapon with the heavy thrown or the light thrown property counts as a ranged weapon when thrown” (Player’s Handbook 215). (Similar text is absent from the Rules Compendium, but I’m not familiar enough with 4e to know if this absence is an issue.)

With this in mind, if a character who has proficiency with military melee weapons but lacks proficiency with military ranged weapons throws a handaxe—a military weapon—, does the character still receive his proficiency bonus on the attack roll?

That is, when a military melee weapon is thrown does the military melee weapon remain a melee military weapon therefore the character above gains his proficiency bonus with it? Or does the thrown military melee weapon now count as a military ranged weapon therefore the character above does not gain his proficiency bonus with it? Or is this even more—or less!—complex than I’m imagining?

Note: My level 3 battlemind who has Strength 10, Dexterity 12, proficiency with simple and military ranged weapons, and proficiency only with simple ranged weapons will still normally make his ranged basic attacks with daggers—preferring accuracy to damage—, but I want to assess my future options just in case. Also, I know I’m late to the party, and I apologize if this is a topic that’s already been discussed to death elsewhere.

Do you add your proficiency bonus when attacking with the Sun Blade if you’re proficient with shortswords only?

The Sun Blade mentions proficiency twice in its description.

The first one is about being proficient with shortswords or longswords:

If you are proficient with shortswords or longswords, you are proficient with the sun blade.

The second one is about proficiency with a longsword:

Proficiency with a longsword allows you to add your proficiency bonus to the attack roll for any attack you make with it.

So what happens if you are proficient with shortswords but not longswords? Do you add your proficiency bonus to the attack roll or not? The first one assumes “yes” since you “are proficient with the sun blade”, but the second one is about longsword specifically. Is the second one just redundant?

Warlock Pact of the Blade – Proficiency

The Pact of the Blade feature of the Warlock reads (emphasis mine):

You can use your action to create a pact weapon in your empty hand. […] You are proficient with it while you wield it. […]

It goes on to say:

You can transform one magic weapon into your pact weapon by performing a special ritual while you hold the weapon. […] …it appears whenever you create your pact weapon thereafter. […]

Suppose my human warlock got her hands on a nice +1 warhammer. Normally, she is not proficient with warhammers. If she uses this feature to transform the +1 warhammer into her pact weapon, she can later summon it at will. Am I correct in interpreting that as long as she wields the +1 warhammer as her pact weapon, she is proficient with it? Or does that clause only apply to the “default” pact weapon?

Understanding the Proficiency bump on Level Up for untrained skills

I’m experienced with DnD3.0, DnD3.5, and PF1e, but I am just starting to delve into Pathfinder 2e and I have a question on Proficiency for Skills.

It says when you Level Up your character, you “Increase all of your proficiency bonuses by 1 from your new level”. Does this only apply to trained (or higher) skills? Or does this apply to all Skills regardless of training? If I am untrained, why would my proficiency in that skill go up if I haven’t been training in it.

If you later train in a skill at a higher level, for example my character becomes “trained” in Medicine at Level 5, would the proficiency bonus be +3 (+2 for “Trained” and +1 for the level up to 5th) or would it be +7 (+2 for “Trained” and +5 for being Level 5)? Thematically I would go with the former. If you delay training in something, you don’t instantly become really good at it when you finally do start training.

Is this the same then for other things with Proficiency modifiers, such as Perception, Saving Throws, Weapons, and Armor?

Does proficiency in both simple and martial weapons mean my character is proficient in all weapons?

So I am building my first D&D character, it’s a Barbarian Mountain Dwarf, and I’m trying to figure out what weapons he is proficient with, but in the Barbarian section it says that he his proficient with Simple and Martial weapons. Does that mean he is proficient with all weapons? And if not, then what weapons does it mean?