If you really don't want to create a second object for the background, you can use some Appearance Panel trickery to add one....
Group the lines
Add a new fill in the Appearance Panel
Move the fill below the Contents in the panel
With the Fill highlighted choose Effect > Convert to Shape > Rectangle
Set the Options for Extra Width and Extra Height to ...
The way you have done it with a rectangle behind the group is the way to "fill" behind a "group"- this is done often- you could also group the rectangle with the lines so they could easily be moved around together.
Alternately, you could combine the rectangle and the group of lines into a compound path (Object>compound path>make) so it is all one "object"- ...
What you're trying to do works better for closed, not open, paths. Try this:
Click and drag to select both points at the top where the shapes meet
Go to 'Object → Paths → Join'
Repeat for the lower ends of the shapes (the points at the bottom of the shapes)
You can't remove that in Illustrator, because Illustrator is built around editing vector files, and PNG is not vector artwork, it is a raster format (made of pixels).
You can however, attempt to do this in Photoshop — which works with pixels — using the 'Levels' panel.
The first one, because your reasoning is correct to add more space on the left margin and align to the center of the hexagon in the logo. That's probably what you already knew, since this was posted as the first image.
that white diamond shape under the logo should not be too strong, you don't want that shape to attract too much attention away from ...
First step I would take, would be to get the rough shape of the exterior rectangle. I'll use orange for contrast purposes:
Next, I'll make the two triangles. They're not equilateral, but I'll get the process started with the Star took and 3 points:
Now I'll align the bottom of it with the rectangle, and distort the top until it aligns with one of the ...
The image example you posted looks like a stock image, which has a watermark. I'm uncomfortable showing you how to copy the design, since it would be copyright infringement. It would be less risky to create your own design rather than copy this.
However, such shapes can easily be made with the pen tool, by drawing straight lines, and the corners can be ...
Usually it's the same shape in different color. In real-life, it's the same object moulded from different material and the same logic applies to the icons. There's no distinct gold badge shape and so on.
A simple internet search will tell you no, there aren't universal icons for these 3 badges / tiers. Some will use stars, some will use coins, others will use other shapes depending on: context the icons are being used for, style, preference, etc.
The one (sort of) consistent element is color: yellow-ish for gold, some shade of gray for silver and a shade of ...
You can't get that with the Drop Shadow effect, but instead:
Select your original T shape
Do an offset via Object → Path → Offset Path
Create a copy of the offset shape and ALT+SHIFT+Drag diagonally
Create an Object → Blend between these 2 offset shapes with 'Specified Distance' set to 0
The author is coloring in the fills of those shapes, not the segments on the side.
To use color on the 'segments' (or strokes in AI language), you need to switch to the stroke by hitting X on the keyboard.
Also a good tip is to use the A (Direct Selection Tool) to select individual objects inside a group.
Maybe the shape builder is what's causing your issues. Here I created three ovals using the eclipse tool:
Now, if you press control/cmd + Y and then select your shapes with the direct selection arrow, you can go into outline mode and see where your anchor points are:
If all your ovals are not meeting at the bottom, I would make sure you do the following:
It's unfortunately very unclear in your question as initially written: the "2D" element you've imported - was this an image file, used as a texture, or a vector format such as DWG, DXF, EPS, used to create actual geometry?
In other words, the bounding box we see in your screenshot looks like you've a rectangle with an image with transparency on it - in ...