This left nav menu is another thing. You need to populate the Extra Nav. You can do that by adding the menu into Appearances > Widgets > Extra Navigation.
In the Extra Navigation Widget Area, you can add Menu Navigation and other widgets that you wish.
You to use in the Widget the MailChimp Widget. Also in the MailChimp for Wp form you have needed this code:
<p>
All meals are prepared using only the best ingredients and cooked when you order them.
</p>
<br />
<p>
<label>Email address: </label>
<input type="email" name="EMAIL" placeholder="Your email address" required />
<input type="submit" value="Sign up" />
</p>
I have fixed the issue with the Sticky Menu by editing the Options at Specular > Header > Sticky Menu > Background
Also, the slider seems to fit perfectly on my screen anyway if you want it to lower you have to add some custom code into the Specular > General > Custom CSS Box
.slider#slider-fullwidth {margin-top:20px}
Now the value 20 depends on the margin you want to create from the header.
We are sorry but there are lot of other tickets. Please share with us your online link and wp credentials (private reply) and we will fix and help you to build your website.
