Mechanical Engineering

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1. Energy savings from partial pipe insulation

https://energyfreakshow.com/2013/01/27/dont-insulate-your-hot-water-pipes/ In short, hot water didnot stored in pipes. New Water tanks already have proper insulation.
2. Linear actuator

Could be electromagnetic from solenoid. no current, no magnetic force. energized with current, solenoid produce magnetic force that move the pin laterally. google the term, solenoid actuator. Plenty of commercial product as well.
3. Optimization constraint function ideas

Stress and deflections are primarily function of diameter. Buckling could be said combination of both diameter and thickness. Stiffness (for vibration) primarily function of diameter. Mass (and material costs) primarily function of thickness.
4. Tackles...

Also, adding more pulley means that the vertical movement reduced for each additional pulley. using 1 pulley, F = W, you move F 1 m, you get W lifted for 1 m. using 2 pulley, F = W/2, you move F 1 m, you get W lifted for only 0.5 m. using 3 pulley, F = W/3, you move F 1 m, you get W lifted for only 0.333 m. But mostly, what DrD said.... friction
5. Why all news graduate engineer have to suffer for job

Wait until you work for a while and realize that most the "mechanical engineers" can't grasp the basic concept of mechanics, fluid mechanics and any basic subjects of mechanical engineering. They won't bother about anything that don't involve money. But they positioned higher than you and obviously better salaried than you.
6. Want to know about Go kart Analysis

Vi= 45 km/h = 12.5 m/s Vf= 0 km/h = m/s t = 0.2 sec (industrial standards) m = 5 x m_original = ... (5g thingy) Impulse F x dt = m x (Vi - Vf) Applied load F to front end of the chassis.
7. is this formula ok?

It should be E not E^2. Other than that it looks correct. Established books make mistakes (albeit rarely). Here's for other potentially conflicting reference https://www.machinemfg.com/load-analysis-driven-power-calculation-symmetrical-3-roll-plate-bending-machine/ I've seen very rare occasion where constants do have dimensional units. (I recall a book by Niemann on Design of Machine Elements, the original German edition) Niemann & Hirt, Maschinenelemente Volume 1: Konstruktion und Berechnung von Verbindungen, Lagern, Wellen Volume 2: Getriebe allgemein, Zahnradgetriebe - Grundlagen, Stirnradgetriebe Volume 3: Schraubrad-, Kegelrad-, Schnecken-, Ketten-, Riemen-, Reibradgetriebe, Kupplungen, Bremsen, Freiläufe Never seen it in American books or European books using SI units. There are occasions that constants have dimensional units in practical standards/codes as well. But that's a different story.
8. can pump run with AIR/Gas

Can you use ur feet to write? with some practice you can. It may never be better than your hand writing, but you can have a decent feet writing.
9. Force/Torque on a cylindrical system

I think this problem goes to T = J x alpha = J x dw/dt But yeah, DrD is correct. Without braking torque, since dw/dt =0, this equation is lacking something.
10. How can I manufacture this spiral slide?

I think that was made by 3D printing.
11. Flow visualization on a flat plate

Google these terms: boundary layer laminar flow point of separation

This is a professional engineering report on its own. You can’t expect this for a free.
13. How do I overcome self doubt in obtaining my engineering degree?

Give you perspective from other way. Unlike a PhD program, both for undergraduate and Master degree program, you can’t be failed by your professor (unless you are very unlucky or very dumb). The only reason of failing is you giving up. In PhD program, you could be failed by your professor during your thesis defense.
14. linear actuator rod extension

What your purpose? Additional length means additional applied force and bending moment. You need to check the working stress on the screwed connection.