As an israeli (born and raised), I'll try my best to answer your question with as few English mistakes as I can.
First thing to know is that Blue and White party was a combination of 3 smaller parties (Yesh Atid, Israel Resilience Party and Telem) they joined forces in order to build one bigger party that can form an alternative to Likud.
A few month ago, the party split into 2: Yesh-Atid-Telem and Israel Resilience Party (which kept the name 'Blue and White').
Because of that, you could find many different voices and opinions, mainly regarding security in this party. Telem, for example, holds more of a right wing agenda and Yesh Atid is a bit more to the left.
In my answer I'll address Blue and White party as if it didn't split (the reason for the split has nothing to do with any of your questions so I won't elaborate here).
Now with that in mind, I'll try to answer your questions.
Palestinian freedom of movement
Blue and White party generally supports the 2 state solution.
If the 2 state solution happens, then obviously there will be a Palestinian state with complete freedom of movement within the area of that state.
While that isn't the case, the Blue and White party supports the current situation where the freedom of movement is limited, for instance because of IDF checkpoints.
In general, almost all of the parties in Israel share the same agenda - without the checkpoints and some limitations over the Palestinian movement we will have more terror attacks.
Dozens of attacks in the last years were stopped by the IDF in those checkpoint.
This issue isn't being addressed by the Blue and White platform as it provides no different agendas among most parties.
Palestian freedom to vote to Knesset
Palestians aren't Israel citizens, so they can't vote for Knesset.
Blue and White party doesn't want to make them citizens because then Israel will have to either:
Stop being a democracy (if Israel decides to not allow some of its citizens to vote)
Stop being a Jewish state (if Israel decides to let them vote then it might lose the Jewish majority over time)
This is exactly the reason why Blue and White (and other parties) wants the 2 state solution as they claim this is the only solution that can keep Israel both democratic and Jewish.
So no, Blue and White doesn't want to give the Palestinians a freedom to vote for Knesset, but instead, it wants to give them a state of their own.
state subventions to Israeli settlements
According to its platform, Blue and White states that it will support the settlement blocks. That means, allowing the population that is already living in relatively large settlements (e.g. Ariel) to keep developing (and provide them with resources, such as money and budgets in order to enable them to do so).
Most settlements, especially the large and old ones, were established with the acceptance/awareness of the Israeli governments over the years, so most parties sense some sort of responsibility for them.
That is one of the reasons why even politicians that are against the concept of settlements and in favor of 2 state solution, will allow some settlements expansion.
This agenda is once again shared among most of the parties in Israel.
However, most of the members in Blue and White party believe that no new settlement should be established, especially not in the areas that are surrounded by Palestinians population.
The reason for that, is in order to keep the 2 state solution possible.
In general, the settlements issue, is so broad and there are many more arguments that are being made. I'll stop here cause I don't want to make my answer too mixed up and complicated.
Do these positions clash with those of Likud?
The agendas are very close to each other. In fact, Telem party (which was part of Blue and White is built from people who left the Likud).
The main difference regarding the Likud and Blue and White is regarding Netanyahu.. many citizens in Israel believe that Netanyahu is corrupted (his trial should begin in Jan 21`) and so they have a personal issue with him.
In addition, Blue and White have said many times that they have no problem working with Likud and building a coalition with them (Yesh-Atid and Likud were in the coalition together for almost 2 years between 2013-2015), their problem is personally with Netanyahu.
Has there been any declaration on the status of the Arab citizens after the proposed annexation of West Bank either by Netanyahu or Blue & White?
Not that I know of.
Note that the annexation of West Bank is currently off the table after the normalization agreement with UAE.
Hope that helps.