Please use the below custom CSS code to make the placeholder text bold.

.is-menu input.is-search-input::-webkit-input-placeholder {
   font-weight: 800;
}

.is-menu input.is-search-input:-moz-placeholder { /* Firefox 18- */
   font-weight: 800;
}

.is-menu input.is-search-input::-moz-placeholder {  /* Firefox 19+ */
   font-weight: 800;
}

.is-menu input.is-search-input:-ms-input-placeholder {  
   font-weight: 800;
}

I hope you are well today and thank you for your question.

Please make sure that you have configured a search form in the Menu Search options as shown in the below screenshot.

View post on imgur.com

You can decrease the search bar width by adding the below CSS code in the Custom CSS option of Ivory Search plugin settings on the path Admin Area -> Ivory Search -> Settings -> Settings

.is-menu.default form {
    max-width: 100%;
    width: 200px;
    padding-top: 14px !important;
}

Best regards,
Ivory Search Support

I hope you are well today and thank you for your question.

Currently, this feature is only available for the search menu but I will consider implementing it in the future version of the plugin.

Best regards,
Ivory Search Support

I hope you are well today and thank you for your question.

You are checking it in the wrong place.

Please check it in the plugin menu search settings as shown in the attached screenshot.

Best regards,
Ivory Search Support

I can see the default search bar on both desktop and mobile as shown in the attached screenshots.

Please advise.