Hazrat Shahjalal International Airport provides an explanation of what is dutiable and a detailed list of what is duty free (which includes your shopping list items).
Duty and Tax Free Goods
You might have already learnt about the rates of duties for various goods when brought to Bangladesh. It is not that you will have to pay duties or taxes for everything you bring with you. There are so many items for which Customs Authority at the airport will not charge any duty or tax.
One thing should be kept in mind, this customs duty free facility is applicable only for non-commercially brought baggage items, that is, items you bring with you, not as cargo. Most of the items brought separately through courier service may require to pay import taxes.
As per the Customs Rule 3(5), 3(7) and Rule 10, following items are considered Duty and Tax free goods. (Duty and Tax are to be paid for commercial quantity import.)
(a) Cassette Player/Two in One
(b) Discman/Walkman (Audio)
(c) Portable Audio CD player
(d) Desktop/Laptop Computer (with one UPS)
(e) Computer Scanner
(f) Computer Printer
(g) Fax Machine
(h) Video Camera (without HD cam, DV cam, Beta Cam, & Professional Camera)
(i) Still Camera/Digital Camera
(j) General Push Button/Cordless Telephone Set
(k) General/Electric Oven/Microwave Oven
(l) Rice Cooker/Presser Cooker/Gas Oven (with Burner)
(m) Toaster/Sandwich Maker/Blender/Food Processor/Juicer/Coffee Maker
(n) General and electric type-writer
(o) Household Sewing Machine (Manual/Electric)
(p) Table/pedestal Fan/ Household Ceiling Fan
(q) Sports materials (For personal use only)
(r) 100 gm gold or 200 gm silver ornaments (Not more than 12 pcs for each item)
(s) One Carton of Cigarette (200 sticks)
(t) Upto 21” Plasma, LCD, TFT, LED Television & upto 29” (CRT) Black & White/Color Television
(u) VCR/VCP
(v) General CD & with 02 (two) speakers Component (Music Center (CD/VCD/DVD/LD/MD set)
(w) 4 speaker component (Music Center) CD/VCD/DVD/LD/MD/ Blue ray disc player
(x) LCD Computer Monitor up to 19” (Either having TV function or not)
(y) Two Mobile/Cellular Phone set