Hi Whammo,
First, do not worry about asking any questions, i am happy to answer or to address them when necessary with updates. 
Colonization 101:
You need a colony fleet with a Colonization Ark in it, when such a fleet is selected then there is going to be an action button labeled COLONIZATION TARGET, use that button to select a target system, it can be an already owned or a neutral system.
As long as the system is explored as in another fleet already visited than you will be allowed to select a planet to colonize using the minimap of the colonization menu just as shown above.
When a target planet is selected then the name of that planet is offered as the name of the new colony, you may change it here or latter from the colony menu. Anyhow beside the colony name there is the COLONIZE button, when hovering over and if the fleet does not carries the minimum number of colonists as well as resources for housing, industry and agriculture then a tooltip reminds the player how much of each is needed, coloring the amount in red if has not enough and in green when it has.
Loading a colony fleet can only be done from the orbit of one of your owned system indicated by the cargo icon in between the 4 button, when the fleet is not in one of your system then it is indicted as shown above and you are unable to click on the loading buttons.
The bar beside the name of the fleet is indicating the carrying capacity and to what degree the fleet is full, if you want more capacity than add freighters to your colony fleet.
Note: Starting a colony with only the minimum amount of resources is not optimal. Also carrying not enough housing and agriculture to cover population growth can lead to protests next turn.
P.S.: The Colonization process is also described in the built in Wiki.
Question 2:
Without knowing exactly why you go bankrupt let me tell you how i was thinking about money when designing the financial aspect of the game. I always thought of the money that you get at the beginning of each turn is your budget for that turn and you meant to use it all up on development only saving for the next turn when you saving for something expensive like a new station, shipyard or a fleet.
Eraly at the game 0-150 turn the game is all about growing your population to facilitate that you have to sink quite the amount of money into colonial development housing, agriculture and industry, but as your population begins to grow on your new colonies you will reach a tipping point when the money from taxation will outweigh the money sinked into growing. To speed the process i suggest to get the technologies that increases growth and pick your first planets with positive Population Growth EV Factors.
To see where you money goes take a look at the Government menus financial breakdown.
Question 3:
For strater read the Wiki's Research Projects that outlines some key features regarding research, like setbacks, disasters and EUREKA. To answer your question yes you pay as you go, each turn based of how much research capacity you allocate toward a project you have to pay for it.
To start a research project you first must select an available tech from the tree and then hit the RESEARCH TECHNOLOGY button left bottom corner, which will create a project in your projects list. If the button is greyed out that means you did not researched the prerequisite technology for that tech indicated by the arrows.
Note: You cannot research a tech twice so if you select a tech that has been researched already the button to start a project will be greayd out.
Regarding monitoring research progress, the 76.2% value above indicates how much has been researched the +5.0% indicates the progress it will make comes next turn the 100% indicates how much you working on it anything above 100% is considered to be rushing the project which has consequences of chance for setbacks and or disasters. The rest is obvious the amount of research capacity allocated and how much it costs.
NOTE: If comes next turn and you do not have enough money to pay for the 1500 capacity then the system automatically reduces each projects used capacity one by one to the point where you can afford it. This rule also applies to colonial development.
I hope this helps a bit, it might seem daunting but i designed it so you can only do things that are valid, i try to guide the player by greying out buttons based on when they can be used or when applicable indicating things through tooltips. Figuring these things out is part of the journey for the player, which does not means that your feedback is not crucial for me to get it right, so you do not need to apologize, you do not bother me at all. It might takes me a bit of time to compose an answer and i also have a nightshift to go to work but i will gladly do it
Have fun and enjoy!