DSO in a 60mm telescope

Question

I am thinking about buying a telescope, but here in Brazil they are very expensive and hard to find where to buy. So, the better telescope I can pay for is a Celestron Powerseeker 60AZ. My main application would be to see nebulas and some star clusters, but I don't know if this scope can be used for this pourpose. Will I see big blurry images, faint lights (like a tiny fog on the darkness of the sky) or only its main stars?

*Note: I've found some images about planets in small scopes on YT, but I haven't found about DSOs (although, I know the images won't be so atractive like bigger telescope ones). Also, can I use the star diagonal as a barlow lens?

Specifications:

Optical Design: Refractor

Aperture: 60mm (2.36")

Focal Length: 700mm (28")

Focal Ratio: 12

Focal Length of Eyepiece 1: 20mm (0.79")

Magnification of Eyepiece 1: 35x

Focal Length of Eyepiece 2: 4mm (0.16")

Magnification of Eyepiece 2: 175x

Finderscope: 5x24

Star Diagonal: 1.25" Erect Image Diagonal

Highest Useful Magnification: 142x

Lowest Useful Magnification: 8.57x

Limiting Stellar Magnitude: 11.4

Resolution (Rayleigh): 2.32 arc seconds

Resolution (Dawes): 1.93 arc seconds

Optical Coatings: Fully-Coated

Optical Tube Length: 711mm (28")

Barlow Lens: 3x

Answer 1

To know what you would see with a telescope, you can use a field of view calculator such as this one from astronomy tools. There, you just fill in the details of your optics, and you can get an idea of what you would be able to see with your telescope.

For a Celestron Powerseeker with the focal lengths and apertures you provided, and a 3x Barlow, the Crab Nebula might look something like this

The yellow line here is the edge of the field of view. You can also use the web app to compare several different configurations. This will give you an idea of how big the object will be in your telescope.

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An other factor to take into account is how bright you will be able to see the object. This depends greatly on where you will be observing (near a city or far away from any bright lights). In any case, the contrast will not be as stark as in the above image.

For this, you first need to estimate the magnitude of the faintest objects observable with the naked eye where you expect to be observing. If you know how to recognize a few constellations, you can look up (in a sky atlas or online) the magnitude of the faintest stars you see. For instance, if you can see M13 in Hercules, then the limiting magnitude with your naked eye is higher than 5.8. However, if you can't see the entire wings of Cygnus, then the limiting magnitude is between 3 and 4.

Once you figured this out, you can use a limiting magnitude calculator. This will give you an idea of the faintest objects you can see with the telescope.